Polite:
- (something) 를 좋아합니다 is "I like ____"
(~rul joh-ah-ham-ni-da)

You can also add 저는 (Joeh-noon) in front which means 'I' (formal way).

Informal:
~를 좋아해
(~rul jo-a-heh)

~를 싫어해
(~rul shil-a-heh)

Here, too, you can add 나는/난 (Na-noon/Nan) which also means 'I' but mostly used when speaking to someone younger or you know very well.

And your examples can be translated as:
I like video games =
(Polite)저는 비디오 게임 좋아합니다
(Informal)난 비디오 게임 좋아해

Hope I helped