"Yet" means "before now" but we only use it with negative sentences and questions:

I haven't finished it yet.

Have you seen it yet?

When people use the word "yet", it usually goes with the perfect form of a verb, like "has done", "has been", "has ___en", and so on.

They haven't started yet, have they?

Have any of you bought one of the new iPhones yet?

In very casual English, people sometimes use the simple past:

Did you buy an iPhone yet?

But a lot of English speakers don't speak this way, and it wouldn't be considered correct grammar in written English.