～の

の after a verb or an adjective turns the phrase into a noun, so it can take は, が or を: "running", "eating", "studying". A verb or い-adjective takes の in the plain form, past or present; a な-adjective takes な.

The phrase before の can have its own subject, marked with が: かれ彼がうたう歌うのをきいた聞いた, "I heard him sing".

の or こと

こと also turns a verb into a noun, and with words like すき好き, たのしい楽しい or むずかしい難しい either one works; の is more casual.

With verbs of seeing and hearing, and with まつ待つ and てつだう手伝う, only の works, because you see, hear or wait for the action as it happens.

Before です, only こと works.

• × 趣味は本を読むのです → 趣味は本を読むことです

の at the end of a sentence

A の that ends a sentence is the casual form of のです: it asks for or gives an explanation. That is a separate grammar point.