I'm nowhere near a great Walgreens shopper, but I did some deals this week. My Walgreens accepts internet coupons. You can use the RR on a second purchase, but if you are going to use it to get RR back, the one you use can't be from the same company as the one you are buying. For example, you can't use the Colgate RR to buy Colgate again and get RR again, but you can use it to buy 2 Visine and get the Visine RR.
You don't need a card at all, the RR prints out from a machine next to the register. I find it complicated, especially trying to figure out what to use the RR for to get some back. And, I pay tons more tax at Walgreens than I do at CVS for some reason. This week, I did:
2 Visine AC ($3.99 - $3 coupon - $3 coupon)
get back 3 RR
1 Colgate ($3.49 - $0.75 coupon)
1 item to get above $3
use 3 RR, get a $3.50 RR
I wanted to buy some Skintimate that was giving back 3 RR, but it was unmarked and the one I bought didn't give me anything, so the game ended for me
I think that Visine and the Reach toothbrushes might be the same company. Also, the RR count as a coupon, and you have to make sure that you have at least the same number of coupons as items.
I also understand that they have monthly RR deals, but they aren't marked at Walgreens here, so I have no recourse to complain if they don't print out.
Good luck, I hope you have a great Walgreens.