Everyone's theory of organization is different. I'll share how I organize my pile just so you can become familiar with the idea, you may find a method that differs from mine that you prefer, and that's okay! :)
When I purchase my Sunday papers I separate my inserts;
Smart Source, Red Plum, P&G (occassionally we'll get a separate insert; Unilever, General Mills, etc..)
I then take a sharpie marker and date the front of each one (mm/dd).
Afer all of my inserts are dated I then stack them in a deep office desk drawer in chronologial order.
When the sales ads come out I cut them as I need them. This works for me. I usually purchase 4-6 papers each week. If it's a good week then I'll get 10 or more. So, you can see how time consuming it would be to clip every coupon each week! I keep each weekly insert about 4-5 months then go through them and discard into the "expired" pile.
By no means is this the best way. This is just what works for me. But if you don’t have a good system you’ll get frustrated by the vast amount of coupons stacks and then possible give up or miss out on deals. So if my way doesn’t work for you, ask around. Look on other blogs or Google. You can easily find other options that will work better for you!