I have a drawer in my house dedicated to coupons. This is also where I put ads, rebate info, gift cards etc.
I have a small binder that I put clipped coupons, catalinas, coupons I receive in the mail, coupons that I know I will use.
It is divided into tabs. The division I use are the next three months expiration, 5 stores categories (Albertsons, Fred Meyer, KMart, Walgreens, and Rite Aid) for store coupons, baby, and anything that expires in more than three months. I use this method because it is easy for me to see if there are any coupons I want to use before they expire. I have also seen alphabetical by brand and food categories or store areas (for example, health & beauty, frozen, snacks, dairy, etc...) These last two work better if you take your binder to the store, which I usually don't do.
I don't "clip" every coupon that comes in the paper. Instead I put them in a folder and then if I need one, it is much easier to find then hunting through my huge stack. I do clip any "high value" coupon that I might use, products I know we will use (such as diapers, juice), any "free coupons", or anything I might like to try, but for the most part they stay in the inserts. I used to clip what products I would usually buy and throw the insert away, but a lot of coupons I needed later I didn't have when I did this. Now I just save them all so if I need them I have them. I keep about 4 months worth in my folder. Every few weeks I go through the oldest inserts and clip the ones that aren't expired yet (which is not very many) and throw the rest away.
When I go to the store, I take the coupons I need (sale matchups) and ones that might expire soon(to look for a possible sale). I also take a list and put it all in just a plain white envelope. I take time to plan out my trip, but this makes it so much smoother when you get to the store. Planning is the next step