You start by humming the first note of the song. This is marked as an asterix (*) in the code. Then you hum the next note. Is it higher (U) or lower (D) or the same (R) as the first note? You write down the appropriate letter. Then you continue to the third note, U, D, or R? You keep going, recording the general notes until you have a code like *RURURDDRDRDRD (Hum it, you'll recognize it). You could then look up the code in the book and find the song.
I thought it was kinda cool. Here's the wiki page for it. Give it a try, if you want, and post it in a comment. I'll try to guess the song.