In order to learn a shout you need to take words from word walls and infuse them with dragon souls which have been absorbed from dragons you have killed.
There are 20 Shouts total which can be learned over the course of the game.
After using a shout, there is a small delay before you can use another. This is indicated by a glow on your compass: when the compass returns to normal, you can shout again.
Each Shout is made up of three words. You must learn these words by finding Word Walls scattered throughout the world. After learning a word, you must unlock it with a dragon soul before you can use it. Dragon souls are absorbed by slaying dragons.