1 slight knowledge of music
Let's get started! This is a lot easier if you are a girl or a guy with a particularly high singing voice, but do not be discouraged. It is rather easy to get to do this.
Step 1: Define your voice type.
I suggest this only for sopranos, tenors and altos so that you don't hurt your voice. I myself are a middle soprano, so I can do all of the ponies, with the exception of Rainbow Dash and Pinkie Pie. My voice just doesn't do that. Here are a few suggestions of voice types for ponies.
Fluttershy- Light and airy Mid Soprano
Dashie- Guy-like Alto/tenor
Rarity- Pompous High Soprano
Twilight Sparkle:Brainy Alto
Applejack- Country slur Mid to low soprano
Pinkie Pie- Energized VERY high soprano.
Pick your pony accordingly.