Although I would to be one of those extreme coupon people on tv, I have developed a system that's short and quick and works for me.
I start off by going to coupons.com smartsource.com and my favorite moneysavingmom.com where I check out the regional stores deals.
I usually do this on Tuesday, since my favorite store changes it's sales on Wed. The best part about this, is when you find your favorite store on moneysavingmom.com people have done the work for you with matching sales with coupons, and even have links to printable coupons!
Also, search google for coupons on brands/items you are looking for, make sure to put the current month and year to narrow down your search such as "laundry detergent coupon July 2011" or "x brand coupon July 2011" you will be surprised how many brands are running coupons but you can't find them on the above sites.
Next, avoid using the coupon right away. It can be tempting, but I try to wait for a sale on the item or closeout price. If it gets close to the expiration date, then go ahead and use it if its something you normally purchase - remember, just because there's a coupon for an item doesn't mean you have to purchase it.
Finally, look at coupon policies, you would be surprised that some stores will take competitor store coupons and even double coupons.
I hope this was some helpful advice to someone and that they can start saving some money in these hard times.