Learn German: Warst du gestern hier? - Were you here yesterday?

bist is the present tense ("are"), but this sentence is in the past tense because it talks about gestern (yesterday). warst is the simple past form of sein (to be) that matches du (you, informal). It means "were".

Why is warst at the very beginning of the sentence?

In German, just like in English, you form a yes/no question by putting the verb in the very first position. If this were a regular statement, it would be Du warst gestern hier. (You were here yesterday). To ask a question, you simply swap the verb and the subject: Warst du gestern hier?

Could I say Warst du hier gestern? instead?

People would understand you, but it sounds unnatural. German has a very common rule for the order of details in a sentence: Time usually comes before Place. Since gestern (yesterday) tells us when and hier (here) tells us where, the time word gestern comes first.

How would I ask this same question formally?

If you were speaking to someone you don't know well or someone in authority, you would use the formal "you" (Sie). The simple past form of sein (to be) for Sie is waren. So, the formal version of this sentence is Waren Sie gestern hier?