My personal coupon organizer is an accordion binder/folder.
It works for now, but as you can see, I'm beginning to bust out of it! It would be a great way for a beginner to start though! I have each section categorized and then use envelopes to sub categorize as such.
Dental floss, toothbrushes, toothpaste, mouthwash
Cosmetics/Hair body wash/soap, Olay products, lotions, mens, shaving, deodorant, makeup, shampoo/conditioner, feminine care
Cleaners/Paper Products paper products, dish products, sponges, plastic, laundry, batteries/light bulbs, household cleaners, air fresheners
Medicine chap stick, eye drops, stomach, vitamins, cold/cough, pain relievers
Baby baby food, diapers/wipes, wash/lotion
Dairy milk, eggs/butter, yogurt, cheese, Pillsbury products (I know...their not dairy, but they are refrigerated!)
Jar/Can oil, canned, salad dressing, condiments
Rice/Pasta/Spices spices/marinades, pasta, pasta sauce, salsa/Mexican, rice
Breakfast/Snacks Peanut butter/jelly, coffee/tea, bread, snack bars, candy, juice/soda, crackers/cookies, chips/pretzels/nuts, cereal
Baking Baking mixes, misc. (I should really rework this category and the breakfast/snacks category as the breakfast one is bursting and the baking one has few coupons in it.)
Frozen pizza, entrees, ice cream, vegetables
Meat/Produce/Restaurants self explanatory
Like I said, this is a great way for a beginner to start! For the more advanced, Crystal at Money Saving Mom has a really great way for organizing coupons. I think I may be switching to that soon.
Other "couponers" use binders with trading card pages and organize their coupons by brand or even by coupon. Like I said, there is no one right way. Whatever works for you. Also, what works for you at one point, may change or you may find you just keep tweeking it.
So, now that you've got your coupons, start organizing!