What it means
のが好きです expresses that someone likes doing an action. It attaches to the dictionary form of a verb, followed by のが好きです. The nominalizer の turns the action into something that can be liked. The polite ending is suitable for standard polite speech, while のが好きだ is the familiar counterpart.
Usage note
のが好きです describes liking an activity, such as reading or cooking. To say that someone likes a thing or person, use a noun directly with が好きです instead, such as 音楽が好きです.
How to use it
Verb (dictionary form)のが好きです
私は音楽を聞くのが好きです。
I like listening to music.
Verb (dictionary form)のが好きだ
私は音楽を聞くのが好きだ。
I like listening to music.