좋다 is an adjective meaning something is good or pleasing, and what you like takes 이/가: 커피가 좋아요. 좋아하다 is a verb meaning to like, and what you like takes 을/를: 커피를 좋아해요. 싫다 and 싫어하다 split the same way.
Examples
- 저는 커피를 좋아해요.
- I like coffee.
- 이 노래가 정말 좋아요.
- This song is really good.
- 저는 매운 음식을 싫어해요.
- I do not like spicy food.
The mistake to avoid
Mixing the particles is the commonest error: 커피가 좋아해요 is wrong.
Where this fits in
좋아하는 것, Korean A2: Talk about hobbies, likes and dislikes, and free-time plans.