が

subject marker

Marks the subject — who or what does something, or what is being described — especially when it is new information or the focus.

Readings

How to form it

Put が after the subject: 猫(ねこ)がいます (there is a cat).
Question words take が, and so does the answer to them: 誰(だれ)が来(き)ましたか — 田中(たなか)さんが来(き)ました.
In a clause that describes a noun, the subject takes が, not は: 私(わたし)が作(つく)ったケーキ (the cake I made).
Some words mark with が what English treats as an object, including 好(す)き, 嫌(きら)い, 上手(じょうず), 分(わ)かる, ほしい and できる: 猫(ねこ)が好(す)きです (I like cats).

雨(あめ)が降(ふ)っています。

It's raining.

誰(だれ)が来(き)ましたか。

Who came?

私(わたし)は猫(ねこ)が好(す)きです。

I like cats.

は and が often appear in the same sentence: in 私(わたし)は猫(ねこ)が好(す)きです, は gives the topic and が marks what is liked.
Between two clauses, が means "but": 高(たか)いですが、買(か)います. See けど.

はtopic marker
Marks what the sentence is about, often something already known, or a contrast.