How to make music transition in movie trailers? (Read the details!)?

im making a movie trailer for one of my classes and i need help . I Have everything set but i have trouble with music transition. i want to put 3 songs in my movie trailer but i dont know how to end them and start them with a song effect or something,BTW i have basic knowledge or final CUT! (http://www.youtube.com/watch?v=l_9FZ1463sw) this is an example of the music transition im trying to make! Listen to the songs stopping and changing theres a certain swwwoop type of sound before the song starts again and Bang ! when it ends, thats what im trying to figure out how to do! any tips, any programs, any specific name i should search for to make more clear what im looking for?