I appear to have lucked into answering the questions for getting into the Thieves' Hideout right on my first try, just by picking things that sound thief-y. There must be some in-game way to actually figure out what the correct answers are, though. Or is it just trial and error? (There are only 9 possible combinations of answers, after all.) What is the penalty for getting it wrong?
There are a few villagers in the town that will tell you the lyrics to the song that they ask you the questions about. The people you need to talk to are in the Milk Bar (the bard), the Veteran Thief's house (in the center of town), and in the merchant's shop (in the top left of the town). They will each give you one line to remember, and then you will have the answers for the questions you are asked.
If you get it wrong, there isn't much of a penalty, they will just tell you something about you not being ready or right, or something to that effect (I forget the exact wording), and you will have to talk to them again to try answering them again.