You can unlock most characters in one of two ways:

Spend 100 gold in the lottery to receive a random character.
Spend $0.99 in real-world money to unlock the specific character you want.

In-game gold is earned a number of ways. You will receive some as you regularly play, and you can find it in the field as you complete your runs. If you like, you can even watch short ads to receive additional gold, so there's no need to ever spend real-world money if you're patient.