What is the Arminian view of God's providence? Disclaimer: This question is not intended to suggest that God is not sovereign under Arminianism. It is simply a question for clarification, as I haven't really found a detailed description. Also, I have read this question but it's not quite what I'm asking.

When I ask "What is the Arminian view of God's providence", I am not referring to soteriology (specifically, at least - it would be included) but to how God brings about His plan, or any given part thereof. Say God decides he wants to bring X about - how does he 'arrange' things to achieve the desired outcome? 

For example, a Reformed Christian might say that God determines things and need not take into account free will so can easily bring about X, while a Molinist would say God arranges the circumstances so humans will freely act in a way that brings about X. Is this within the scope of Arminianism? What level of detail do Arminians say God's plan has? Does it include individual human actions? I realize that's several questions but they all fit within this one/are details that I would hope to be included in the answer to the main question.
General backround

I am going to quote from one prominent Arminian theology advocate, Roger E. Olson, a well-published professor of theology and ethics.  One of his books is the 2006 Arminian Theology: Myths and Realities.  He maintains a blog called My Evangelical Arminian Theological Musings.  In this March 2014 blog article Arminianism and Providence I think he addressed all your subquestions while omitting the soteriological aspect (as you requested) because he helpfully contrasts many elements you mentioned that are connected to providence: free will, God's will, sin/evil, foreknowledge, foreordaining, etc. although the blog article may not be to the level of details you are looking for.

Some quotes from that article:


  
  I have expressed my own overall view of God’s providence this way: “God is in charge but not in control.” However, some Arminians objected to that.
  Sin and evil are included in God's consequent will, not God's antecedent will.  God governs them but does not design, foreordain or render them certain. ... The only category of creaturely decisions and actions where God NEVER interferes with free will IN THE SENSE OF rendering them certain is sin and evil.  God permits them but does not design, foreordain or render them certain.  ... In relation to creaturely decisions and actions that are sinful, God never designs, foreordains or renders certain individuals’ evil decisions and actions that would cause their condemnation.
  God DOES interferes with free will in guiding and directing our lives as his people.  He is not the author of our sins or failures, but he does direct our lives in terms of opening and closing doors.
  If we shut him out of our lives and tell him to leave us alone he will, saying, reluctantly, "Okay thy will, not mine be done." This, too, of course, is within his will -- consequently but not antecedently.
  ... he foresees their sinful intentions and allows me to be in the path of their consequences insofar as that “needful and best” for me.  ... Much of what I suffer may very well be his will. I do not expect God to be “fair” to me or keep me from harm (although I believe praying for him to preserve my life and help me in times of trial is always good).
  


I think more details would be forthcoming from his two books, both highly rated in Amazon:


Arminian Theology: Myths and Realities (2006)
Against Calvinism (2011)


Details on how God "arrange" things


  Say God decides he wants to bring X about - how does he 'arrange' things to achieve the desired outcome?


Answer: by 


"placing people in circumstances where he knows what they will freely do because he needs them to do that for his plan to be fulfilled."
divine self-limitation so as not to be the cause of evil


God truly respects human freedom even to the point of reluctantly allowing evil to happen, which thwarted His perfect will, but then He work around them to orchestrate His plan because He foreknew the outcome of those evil actions.  "He has chosen to make himself partially dependent on his 
human covenant partners while remaining the “superior covenant 
power of holy love.”".  Thus He chose not to force miracle to happen in Nazareth but making it dependent on people's faith.  Thus He allowed Jesus to be crucified although He didn't tempt the people who made the decisions to sin but working around them to achieve the final result.

Basis for the answer

The answer above was based on Chapter 4 ("Yes to God's Sovereignty; No to Divine Determinism") of his book "Against Calvinism" referred to above.

Plan for Chapter 4.  After starting with 2 heart-wrenching examples to illustrate the insufficiency of Calvinistic divine determinism, he wrote a long historical summary of Calvinist teaching by discussing in individual sections the treatment by Zwingli &amp; Calvin, Jonathan Edwards, Loraine Boettner, R.C. Sproul, Paul Helm, and John Piper.  Then he discussed in a section titled "The Problem of God's Reputation" quoting evangelical philosopher Jerry Walls who says "The Calvinist must sacrifice a clear notion of God's goodness for the sake of maintaining his view of God's sovereign decrees."  In the next section "The Freedom of God and Human Responsibility" he discussed the view of the various Calvinists focusing on this topic.  Finally he closes with the section "Alternatives to Divine Determinism" from which I constructed the short answer above.

Quotes from the final section of chapter 4 (emphasis mine):


  ... The main alternative to this strong doctrine of God’s sovereignty [i.e. Calvinist doctrine of divine determinism] is divine self-limitation.
  
  First, let it be clearly understood that those who appeal to divine 
  self-limitation and passive permission as the explanation for sin and 
  evil in the omnipotent, creator God’s world do not say God never manipulates historical circumstances to bring about his will. What God 
  never does is cause evil. God may and no doubt sometimes does bring 
  about some event by placing people in circumstances where he knows 
  what they will freely do because he needs them to do that for his plan to 
  be fulfilled. Such seemed to be the case with Jesus’ crucifixion. Even 
  then, however, it was not that God tempted or manipulated individuals 
  to sin. Rather, he knew what events, such as the triumphal entry, would 
  result in the crucifixion.
  
  But what we must not say is that the fall of Adam, which set off the 
  whole history of sin and evil, was willed, planned, and rendered certain 
  by God. God neither foreordained it nor rendered it certain, and it was 
  not a part of his will except to reluctantly allow it. How do we know this? We know it because we know God’s character through Jesus Christ. 
  The doctrine of the incarnation proves that God’s character is fully 
  revealed in Jesus such that “no interpretation of any passage [in the 
  Bible] that undercuts the revelations of the divine mind inculcated by 
  Jesus can be accepted as valid. What he says and does is what God says 
  and does. He had no hidden decrees to conceal, no dark side of his 
  Father to protect from disclosure, no reason to be defensive about the 
  [ways of] God.”¹⁰⁵
  
  The high Calvinist doctrine of God’s sovereignty including evil as 
  part of God’s plan, purpose, and determining power blatantly 
  contradicts Scripture passages that reveal “God is love” (1 John 4:8), 
  takes no pleasure in the death of the wicked (Ezek. 18:32), wants 
  everyone to be saved (Ezek. 18:32; 1 Tim. 2:4; 2 Peter 3:9), and never 
  tempts anyone (James 1:13). To be sure, Calvinists have clever but 
  unconvincing explanations of these and numerous other passages of 
  Scripture. For example, John Piper argues that God has “complex feelings and motives,”¹⁰⁶ such that he genuinely regrets that sin and 
  evil have to be part of his world, genuinely wishes that all people could 
  be saved, and is grieved when those he predestined to die and even 
  suffer in hell for eternity for his glory experience that fate. But these are not convincing explanations of these important passages that reveal the 
  heart of God. They make God double-minded.
  
  So how might one deal with the reality of sin and evil in God’s world 
  without placing undue limits on God’s power and sovereignty? The 
  only way is to posit what Scripture everywhere assumes — a divine 
  self-limitation in relation to the world of moral freedom, including 
  especially libertarian freedom. That freedom is a wonderful and terrible 
  gift of God to human persons created in his image and likeness. In 
  other words, God allows his perfect will to be thwarted by his human 
  creatures whom he loves and respects enough not to control them.
  
  Thus, God does have two wills, but they are not ones posited by 
  Calvinism. As a result of Adam’s free choice to fall into sin (with free 
  choice here meaning he could have done otherwise), God has a perfect 
  will— also known as his antecedent will. (“Perfect” here means “what 
  God truly wishes would happen.”) God’s perfect will is that none 
  perish; this is God’s antecedent will (antecedent to the fall and to its 
  resulting corruption in the world). God also has a consequent will— 
  consequent to creaturely rebellion. It is that he allows some freely to 
  choose to perish. But his allowing is genuinely reluctant and not 
  manipulative.
  
  Evangelical theologian Stanley Grenz (1950 – 2005) offered a helpful 
  distinction in God’s providence that corresponds to the two wills — 
  perfect/antecedent and consequent — mentioned above. It is the 
  distinction between “sovereignty de facto” and “sovereignty de jure.”¹⁰⁷ According to Grenz, with whom I agree, due to God’s voluntary 
  self-limitation he is now sovereign de jure (by right) but not yet 
  sovereign de facto (in actuality). His sovereignty de facto is future. This reflects the biblical narrative in which Satan is the “god of this age” (2 Cor. 4:4) (where “world” clearly means “this present evil age”), and God 
  will defeat him in the coming age to become “all in all” (1 Cor. 15:28). 
  The entirety of 1 Corinthians 15 can be interpreted in no other way; it 
  assumes the distinction between God’s sovereign rule de jure now and 
  de facto in the future. This is not to say, of course, that God is not 
  actually sovereign now at all; it only says that God is allowing his 
  sovereignty to be challenged and his will to be partially thwarted until 
  then.
  
  Doesn’t this limit God’s power and sovereignty? No, because God 
  remains omnipotent; he could control everything and everyone if he 
  chose to. For the sake of having real, personal creatures who can freely 
  choose to love him or not, God limits his control. Still, God is sovereign 
  in the sense that nothing at all can ever happen that God does not allow. 
  Nothing falls totally outside of God’s supervening oversight and 
  governance. But not everything that happens is what God wants to 
  happen or determines to happen. There is no exhaustive divine 
  determinism.
  
  Of course, Jesus, being God, could have healed everyone in 
  Nazareth when he visited there (Mark 6:5), but he “couldn’t” do 
  miracles there because of their lack of faith. As God, he had the sheer 
  power to do miracles. But he had limited his power ordinarily to do 
  miracles in the presence of faith. He did not want to go around 
  unilaterally healing people without some measure of cooperating or 
  receptive faith on their part. So it is with God’s sovereignty. He could exercise deterministic control, but he has chosen not to do so. As 
  theologian E. Frank Tupper says, God is not a “do anything, anytime, 
  anywhere kind of God” because he has chosen not to be that kind of 
  God.¹⁰⁸ He has chosen to make himself partially dependent on his 
  human covenant partners while remaining the “superior covenant 
  power of holy love.”¹⁰⁹


Footnotes:


  ¹⁰⁵. William G. MacDonald, “The Biblical Doctrine of Election,” in 
  The Grace of God, the Will of Man: A Case for Arminianism, ed., Clark H. 
  Pinnock (Grand Rapids: Zondervan, 1989), 213. 
  
  ¹⁰⁶. Piper, The Pleasures of God, 146. 
  
  ¹⁰⁷. Stanley J. Grenz, Theology for the Community of God (Nashville, 
  TN: Broadman &amp; Holman, 1994), 140. 
  
  ¹⁰⁸. E. Frank Tupper, A Scandalous Providence: The Jesus Story of the 
  Compassion of God (Macon, GA: Mercer Univ. Press, 1995), 334 – 35. 
  
  ¹⁰⁹. Hendrikus Berkhof, The Christian Faith: An Introduction to the 
  Study of the Faith (Grand Rapids: Eerdmans, 1991), 146.


Recommendations for further reading


Del Rey Church Theology class material on Providence, Decrees, Creation.  Del Rey Church is an EFCA church which accepts both Calvinism and Arminianism.  The class material seems to be non-polemic and really tries to let each side states the position well.  I think this is an excellent way to survey various positions regarding Providence.  It's very long and detailed, but I think it's worth studying.
Thomas Oden's book Classic Christianity: A Systematic Theology which is his attempt to present ecumenical Christianity before the fall of Rome (thus before the schism) so not specifically Wesleyan / Arminian.  He limits himself to patristic interpretation of the Bible, which I think is very valuable to learn how the patristic fathers didn't spell out too much specifics on God's providence, leaving it open for later theologians to fill out the detail (which on the negative side can lead to unhealthy disputes that distract us from what's common to Christianity).  He himself is a Methodist, and in his earlier book The Living God: Systemic Theology: Volume One he has more details on the Arminian view of providence and the book was quoted by the class material above.