I use a box and envelopes. Here's my box:
It's a Sterilite box with a lid that snaps on (I keep my coupon scissors in there as well).
I have my envelopes labeled with categories and the categories are sorted by type. I have 6 main categories - Foods that are snacks, condiments and such, Foods that are boxed, bagged or canned, Frozen/refrigerated foods, Household goods (including paper products and cleaning products), Health and beauty, and Medical. Each category is broken down further. Some people find it helpful to alphabetize by company rather than break down by category. Use whatever works. I like having all brands of a certain type of food or item in one place. It makes it easier for me to do comparison shopping.
I buy 4 papers. I take all of one insert and pull out one page at a time - the same one from all 4 copies. I line them up and cut all four like pages at once. As I cut, I put the coupons in front of the envelopes where they are to be filed.
When I am finished, I go through the box and file the coupons in their envelopes. I also pull expired coupons at this time.