Can someone help me figure out how to use new Chase Explorer CC in UA website in order to be sure I qualify for the promos?

I really had no idea how to search for this, so I hope I'm not posting yet another of the same question.

I've just gotten the Chase UA Explorer CC and I'm trying to book flights. I want to be sure I do it so that I get the $400 back promo and the miles applied to my newly created UA mileage plus account.

I feel so dumb with this. I've never done an airline credit card-airlines miles kind of purchase before. Maybe it's quite simple and I'm just not getting it.