When people find out that I'm an "extreme couponer" the first question is always, "How do you do it?!" I feel that everyone is different, and it all depends on how much time you are willing to put into couponing. The more time you put into your couponing, the more you'll save, and the more products you'll be able to stockpile and use.
So, with that being said, my preference on organizing my coupons may not be the best method for you. It took me a couple years to master the right method for me and my busy schedule. I've tried everything from: clipping only the coupons I think I'll want to use (DON'T DO THIS! lol); or using baseball card holders in a 3-ring binder to hold all the coupons I clipped; or even organizing my clipped coupons based on where the products were placed in the stores: "dairy," "cold," "frozen," "hair products," "cleaning supplies," etc. Now, here's the EASY, and time saving method I use now!
First, I have a large carrying case that I have labeled by months (first half of month, and second half of month). Obviously I won't need all of the months at the same time (no coupon would be good that you bought in January, once September comes!) but it felt right to do it this way for me.

You can purchase one of these pretty inexpensively at Target, Walmart, etc. I think mine was around $5 or so.
Ok, now that is done, on to the coupons! I don't clip them. At. All. "WHAT??!?" Yes, you read it right.. I do not waste hours on end anymore by clipping all of the coupons from the weekly inserts.
I keep them in "magazine" form, and place them in the corresponding month (beginning of the month or later in the month). Then, when I know I'll need to use them for a deal, I find the right insert, find the coupon(s) I'll be using for freebies/cheap deals, and clip it.

About once every month or two, I check on the older coupon inserts and throw out the expired ones. Again, I don't clip anything, but I'll just tear out the good pages, and reinsert them in the correct folder.
If I spot a coupon that I KNOW I'll use, whether the item will be free or not, I go ahead and clip it and place it in an envelope that I keep in the front of my carrying case. This allows me to carry only the envelope to the store with me, and use the coupons on the daily items I purchase. (I do not lug this carrying case around FYI. lol)
I also buy 1-5 newspapers each week, depending on how good the coupons are, or how many inserts there are. If the paper has a SmartSource and another insert like P&G, I'll probably buy 4-5 newspapers. The reason for this is because it allows me to purchase many more things with my extra coupons, and stock pile the items that I get for free. (Yes, you'll get probably $40-$200 worth of freebies every week.) Stock piling is nice for many obvious reasons, but it also helps because at the end of the year if I have too many products that I won't use, I can donate them to local shelters. So, I got the items for free (sometimes I even 'get paid' to purchase them!) I use what I want, and get a tax write off, WHILE donating and helping others. Not a bad deal. ;)
At any rate, this is the easy and organized way I keep track of my coupons! It saves me hours of work from cutting ALL the coupons ahead of time, and it's super easy to find the coupons I need, when I need them. I hope this helps you in some way! Let me know if you have any questions or opinions! Let me know how you stay organized!