Usually the rebate involves filling out a postcard and mailing it with a copy of your receipt to their office that handles rebates, then waiting for them to mail you a check or pre-paid card (usually from Amex, Visa, or Mastercard).
Many have switched to skipping you having to mail anything and instead submitting the data online, then they mail you the check or card.
Unless the rebate is "Instant" you have to pay the full cost up front, then wait for the rebate as reimbursement.