I thought I would go step by step through a Safeway scenario for those of you just starting out.
Here is what the scenario would look like posted online:
Nalley Pickles at Safeway on sale for $2.49 with Club Card thru 5/8
Use (1) 75¢/1 from RP 4/17
Use (1) Safeway Double up to 50¢ Coupon from In-Store Ad or Wednesday's Paper
Final Price: $1.24
Here is what the pricing looks like on the shelf:

On this trip I am going to purchase 4 jars of pickles. I chose four because this is the maximum amount of manufacturer's coupons that Safeway allows me to double up to 50¢ per shopping trip. I check that my coupon matches the product, is not expired, and does not say "DO NOT DOUBLE." This is a picture of the coupons I will use on this trip.
I make sure that I have a current Safeway Double Coupon. These are in Wednesday's Paper, but you can also find multiple copies of Wednesday's ad in each Safeway store. I have never had a problem finding these. They are also in the "Neighbors" papers at places like Prospector's Place and Indy Diner. The Safeway Double Coupon is pictured below. You do not need to fill in amounts.

Have your coupons ready before you get in line. After unloading your cart enter your Club Card # or give the cashier your card when prompted. In some grocery stores, unless you enter your rewards/club card before coupons are taken off you will not meet your maximum savings potential. Watch to ensure that items ring up as advertised. Safeway will ring through your original coupons, in this case 75¢ will be taken off times four and then the cashier will take an additional 50¢ off per coupon doubled.
This is what my receipt looked like after the transaction:
This was a savings of 77%
I hope this helps. If you have any questions/comments, fire away!