This was going to be an intermediate level post, but this phrase is so ubiquitous that a beginner really needs to know it right away. This is one of those phrases that finds it's way into just about every conversation here.
It's the kissing cousin of deixa comigo.
Leave it to me.
I can do it.
Let me do it.
I'll take care of it.
I can handle it.
So, when you say pode deixar, it's really você pode deixar para eu fazer.
But no one will ever say that.
The last example is very advanced. He says:
> Tá. Assim que eu chegar em casa eu vou ler o documento.
> Pode deixar.
The "tá" is just "está bom" = Ok.
Brazilians say tá all_the_time. When said by itself it's always means Ok.