Zaa zaa (ざあざあ) is the sound of heavy, pouring rain: あめが ざあざあ ふって います is “it's pouring”.
Close your eyes during a summer storm. That loud, steady hiss on the roof and the road is ざあざあ.
What it means
ざあざあ is rain coming down hard and without a break. It is also the sound of a lot of running water, like a shower turned up high.
How to use it
Put it before ふります, the verb for rain falling: ざあざあ ふります, ざあざあ ふって います. A downpour itself is called どしゃぶり.
あめが ざあざあ ふって いますね。
It's really pouring, isn't it.
かさを わすれました…。
I forgot my umbrella...
いっしょに かえりましょう。
Let's go home together.
Close cousins
しとしと is quiet, steady rain, the gentle kind of the rainy season. ぱらぱら is a few light, scattered drops. ぽつぽつ is the first drops, one by one, just before it starts. Japanese has a sound for every kind of rain, and ざあざあ is the loudest.
In manga and anime
Heavy rain is drawn as long straight lines with ザーッ or ザアアア across them — very often in a sad scene, with a character standing alone without an umbrella.
Can you use it?
Yes, anywhere. It is how people naturally talk about the weather: きょうは ざあざあ ふって いますね.