The Rundfunkbeitrag is the mandatory contribution from every household to fund ARD, ZDF and Deutschlandradio. The principle: one household — one contribution, regardless of how many people live there.
How to register
Registration is fully online at rundfunkbeitrag.de. You need your personal details and bank account information for a SEPA direct debit. No documents need to be uploaded.
Deadline
This is a legal duty, not a suggestion: § 8 (1) RBStV requires you to report the move-in without delay (unverzüglich). Failing to report the start of liability within one month is a regulatory offence (§ 12 (1) no. 1 RBStV) and can be fined. In practice the advice matches the money side: do it in the first week after your Anmeldung at the Bürgeramt.
Since you are sorting household bills — Grundversorgung almost always overcharges by €200–500 a year