What does "believe the Bible" mean? What do Christians, namely Evangelicals, mean when they say it? To what extent must the Bible be "believed"? Does this connote a literal interpretation of the scriptures, or does this connote a general attitude of how a Christian may view the Bible?
It means to believe the propositions of Scripture to be true. Everyone believes some set of propositions to be true, which they cannot prove. For a Christian this axiom is: That the Bible is the Word of God (and hence is true in what it teaches).

Same applies to any belief....e.g. for a Muslim, they believe the propositions of the Koran to be true. Likewise Hindus believe the propositions of Vedas to be true. Atheists believe the propositions of Bertrand Russell, Dawkins and so on to be true. And if I believed all that your Pastor said (say his name is "Smith") then I would be called a Smithian in my belief.

But a Christian believes the propositions of the Bible to be true. For a person to say they are a Christian but say they don't believe the Biblical propositions is nonsense. A person may not state it exactly that way, but if they do not believe the Bible to be true then all they have left are their own muddled thoughts at least as far as being a Christian is concerned. So the propositions that God made the world, that Jesus is the Son of God, that He died and rose again from the grave and is coming back again, that God is a Trinity of persons etc all these propositions are clearly in the Bible (1 Cor.15:1-4). To believe these to be true is to be a Christian. Not to believe them is to be something else.

You ask, "Does it denote a literal interpretation"?  It depends on the genre of the passage being read e.g. if the genre is metaphorical then the passage needs to be read metaphorically or else confusion will reign. Where it is historical genre, then it needs to be read as history,  poetry as poetic and so on. The Bible is not written in a single genre.