[verb (dictionary form)] + のが好き
のが好き means "like doing". The verb is in the dictionary form, の turns it into a noun, and that noun takes が before 好き. The person who likes it takes は, or is left out when it is you.
English "like" takes an object, which pulls learners towards を. 好き takes が, and the の can't be dropped.
好き is a な-adjective: すき好きじゃない in the negative, すき好きだった in the past. だいすき大好き is "love", and あまり with the negative is "not really". The verb stays in the dictionary form throughout.
ことがすき好き means the same and sounds a little more formal. With a noun there is no の at all: おんがく音楽がすき好きです.