Okay, so...
I actually haven't figured out how to rearrange the order of the songs (or audio files) in my music "Library", but if you create a separate "Playlist" you can.
You'll notice the tab-bar at the top of iTunes, if you're viewing it in the most basic list form. The bar includes items for ordering such as Artist, Song, Album, etc. By clicking on any one of these tabs, iTunes will automatically reorder all of your audio files according to that category (alphabetically by Artist, Album, etc. or numerically by track length, track number, etc.). When you're viewing your iTunes "Library," which shows all of your audio files, there is no option, as far as I can tell, for you to place each file wherever you may want.
However, if you create a new playlist, and throw a bunch of the songs/tracks from your general Library in there, then you can go into that playlist and rearrange the order. These sub-playlists also have the category tabs at the top, but what's different about them is that the very first column is also clickable (whereas it isn't in Library view). Generally speaking, when you pull songs from your Library into another playlist, that playlist will, by default, order those songs chronologically, with the first track added at the top of the list, and each successive track added appearing below it.
If you click on any of the other category tabs, like Artist, then the tracks you've added will be put in order according to that category. If you then click the first column tab again, it will replace them in the original chronological order they were in.
To finally answer your question (sorry for the longwinded reply), simply click on the very first column tab (which will be unlabeled) in that playlist, and you should be able to click-and-drag the tracks in that playlist into whatever order you desire.
I hope this helped!