definitely look for the early edition sunday newspapers. they are not available for all newspapers, but if you can get them they are usually cheaper than the regular sunday edition!
i usually find these at cvs and walgreens on saturday afternoons. you can probably find them in other stores, but i'd much rather spend extrabucks or use my wags register rewards instead of actual cash.
take a moment to flip through and be sure the coupon inserts are all there. it is quite annoying to go out for the paper, get home and realize you don't have any coupons. i check taylortownpreview.com beforehand so i know what inserts should be there. looking at the list of coupons coming out will also help you to decide how many copies you want to buy.
you might find that rather than buy the newspapers, it may be cheaper to order your coupons from a clipping service. since the early edition sunday newsday went up to $2, i have stopped buying it and instead order my coupons from coupon dede. she offers complete inserts as well as clipped coupons. another good place to order from is the coupon clippers.
pull out all the coupon inserts from your papers. i save the rest of the newspapers for a couple of days. (i do this because once i threw them out immediately, and the next day i read online that there were cvs coupons in the "a" section!)
now make a stack for each page. i usually sit on my living room floor and spread everything out around me.
i then staple all of the same pages together (put the staple in a non-coupon part of the page.) line them up nicely so that you will be able to clip multiple of coupons at once when you need them.
at this point i will clip any coupons i see that i want to give away. for example, i do not need any pet food coupons or meat product coupons (vegetarian) so i put those into an envelope for my mom.
reassemble pages into one "monster insert" :)
repeat for each insert
i use a box with hanging file folders. label each folder with that sundays's date, preferably with a sharpie, so that it is clear and easy to read.
i keep the newest coupons at the front of the box. each week i take the oldest folder from the back, check through for any coupons that have not expired yet, and throw away the rest. then relabel the folder for the current week.
what about other miscellaneous coupons? tearpads, the old-but-unexpired ones i just took out of my file, internet coupons, ones i clipped but didn't use after all, etc...
i put those into a photo album, alphabetized by brand name.
when i want to see if i have a coupon for a particular item, i use the listing on slickdeals or the couponmom database. search for the brand or product. if you find a coupon to use, note the insert and date listed for it. pull out that date's folder and flip through the appropriate insert for your coupon.