"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.