All you have to do is go to this page, find the hotel you want to book, opt to pay online, and use promo code TARGETREDCARD. You don’t actually have to pay with the REDCard to take advantage of the deal, you’re just supposed to have one.
The big key here, like most Hotels.com deals, is that you have to pay in advance, even if that doesn’t result in a discount compared to the rate you’d pay at the hotel. Promo codes can’t be applied to stays that you pay for at the hotel. Other terms and conditions apply, which you can check out here.