Welcome to Gaming SE!
You have to unlock each word individually with a dragon soul in order to use it. That way, you can save your dragon souls for later, for the shouts you want, not necessarily the ones you get earlier.
To unlock a word, go to Magic -> Shouts, move the mouse/selection over the shout you want to unlock, and press the required button/key, displayed in the lower left.
Each shout has 3 words, and you automatically unlock them in order. Of course, you need both a dragon soul and the next locked word in a shout to advance that it.