So, here's how it works:
1. Open your library (iTunes, Winamp, Media Player, iPod, etc)
2. Put it on shuffle
3. Press play
4. For every question, type the song that's playing
5. When you go to a new question, press the next button

Opening Credits:
My Friend, the Dictionary - The 25th Annual Putnam County Spelling Bee

Waking Up:
The Contest - Sweeney Todd

First Day At School:
Do You Hear the People Sing? - Les Miserables

Falling In Love:
Any Moment/Moments in the Woods - Into the Woods

Fight Song:
Gee, Officer Krupke - West Side Story

Breaking Up:
Ever After - Into the Woods

Prom:
Johanna (Quartet) - Sweeney Todd

Life:
One Hand, One Heart - West Side Story

Mental Breakdown:
That it Should Come to This - Hamlet the Musical

Driving:
Heaven on Their Minds - Jesus Christ Superstar

Flashback:
The Meek Shall Inherit - Little Shop of Horrors

Wedding:
Lament - Into the Woods

Birth of Child:
Pirelli's Miracle Elixir - Sweeney Todd

Final Battle:
Prologue - Into the Woods

Death Scene:
One Day More - Les Miserables

Funeral Song:
Not While I'm Around - Sweeney Todd

End Credit:
Knights of the Round Table/The Song That Goes Like This (Reprise) - Spamalot