Also, the song you mentioned that was turned into a waltz would be in 3/4 time. 12/8 time would still feel like it has four beats.
If a song has a two sub-beat feel (think eighth notes), count "One and Two and...."
If a song has a three sub-beat feel (think triplets), count "One and uh Two and uh..."
If a song has a four sub-beat feel (think sixteenth notes), count "One ee and uh Two ee and uh..."
What Jonathan wrote is right on. But there can be more than one way to notate the same sound. For instance, both of the measures below would sound the same. If the whole song had a triplet feel, the composer would probably use 6/8 time. If just a measure or two in the song had a triplet feel, those measures would be notated like the second measure.
