You already use gostar de with things: Eu gosto de café. Put a verb straight after de — in the infinitive, the form ending in -r — and you're talking about what you like doing:

• Eu gosto de ler. — I like reading.
• A Luana gosta de dançar. — Luana likes dancing.

The question you'll hear is O que você gosta de fazer no tempo livre? — What do you like doing in your free time?

Passatempo
ler	to read
ouvir música	to listen to music
cozinhar	to cook
dançar	to dance
nadar / correr	to swim / to run
viajar	to travel
ver um filme	to watch a film
ir à praia / ir ao cinema	to go to the beach / to the cinema
jogar futebol	to play football
tocar violão	to play the guitar

Portuguese has two verbs for play: jogar for sports and games (jogar futebol, jogar vôlei, jogar cartas), tocar for instruments (tocar violão, tocar piano). A violão is an acoustic guitar.

For films you'll also hear assistir: assistir a um filme — in everyday speech usually without the a: assistir um filme.