Praise and Worship, what is the difference? What does "praise" look like?  How does it differ from "worship"?

We are urged/called to/commanded to praise God (psalms 146:1 and others), but what is it and what does it look like?  

Romans 12:1-2 states: I appeal to you therefore, brothers,by the mercies of God, to present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship.(ESV)
I expect this question will be soon closed as primarily opinion based, but let's sneak in an answer.

Merriam-Webster defines "praise" as:


  1) to express a favorable judgment of
  
  2) to glorify (a god or saint) especially by the attribution of
  perfections


I like to think of praise in terms of a word I like to think is related: raise


  1) to cause or help to rise to a standing position


Because it makes perfect sense to me what Paul wrote to the Corinthians (1 Cor 4:5)


  Therefore judge nothing before the time, until the Lord come, who both
  will bring to light the hidden things of darkness, and will make
  manifest the counsels of the hearts: and then shall every man have
  praise of God.


When we praise God, we lift up His importance in our lives.  It's no suprise that He will do the same for us.

Praise is often a spoken thing.  For example, praise is often given in song.  Hebrews 2:12


  Saying, I will declare thy name unto my brethren, in the midst of the
  church will I sing praise unto thee.


Paul and Silas both sang and praised (Acts 16:25) leading us to believe praise occurs in prayer.  It's disappointing that the only verse that easily makes this connection is from LDS Scripture.  From D&amp;C 136:28 we read:


  If thou art merry, praise the Lord with singing, with music, with
  dancing, and with a prayer of praise and thanksgiving.


See also Psalm 72:15.

The two definitions of worship that are relevant to us are:


  2) reverence offered a divine being or supernatural power; also :  an
  act of expressing such reverence
  
  3) a form of religious practice with its creed and ritual


Worship is a much more complex word.  It involves more than simply speaking.  Also, where praise is the act of lifting another up, worship is the act of lowering oneself in humility before another.  (Rev 19:4):


  And the four and twenty elders and the four beasts fell down and
  worshipped God....


Worship always involves praise, though praise doesn't always involve worship.  Matthew 14:13.


  Then they that were in the ship came and worshipped him, saying, Of a
  truth thou art the Son of God.


Not surprisingly, we can be the recipients of this kind of worship (fundamentally, praise) in regard to other people.  Luke 14:10.


  But when thou art bidden, go and sit down in the lowest room; that
  when he that bade thee cometh, he may say unto thee, Friend, go up
  higher: then shalt thou have worship in the presence of them that sit
  at meat with thee.


Worship describes the act of helping others understand, follow, and worship.  This is reflected in a chastisement given by the Lord (Matt 15:9):


  But in vain they do worship me, teaching for doctrines the
  commandments of men.


And it describes service to the being we worship.  Matthew 4:10.


  Then saith Jesus unto him, Get thee hence, Satan: for it is written,
  Thou shalt worship the Lord thy God, and him only shalt thou serve.


Therefore, praise is something we (usually) say to raise another above ourselves and worship is something we (usually) do to humble (lower) ourselves before another.

An example: from our point of view, if two of us are standing on a stair, one praising the other would encourage the other to stand on the next higher stair.  One worshipping another would willingly and selflessly step down one stair so the other would be a step higher.