Eu gosto de você.

eu-gosto-de-voce

GOSTAR is one of the verbs that you will use all the time.

And there is something different about it in that it is always (always) followed by a de.
Think of it like this: When you like something or someone, you like of them or it.

You like (of) fresh bread, for example.

Você gosta de pão fresco.

You like (of) samba.

Eu gosto de samba.

And if the de is followed by an article, o or a, they contract like this:
de + o = do
de + a = da

You like David. > Você gosta do David.
I like Brazil. > Eu gosto do Brasil.
We like the novela. > Nós gostamos da novela.

The only time the de isn't said is in casual conversation like this:

Do you like to travel?
Gosto!

From INTENSIVO