This is the way I do coupons to save the most money possible. You can do as many or as few steps you see here, depending on time available and amount you want to save. I want to stress that each eliminated step drastically cuts into savings.

Step 1 Choose a way to store your coupons so they stay organized and easy to find. This could be a Rubbermaid™ container, a drawer, a shoebox, an accordian file. Whatever suits you. Use some index cards or poster board parts for indexing depending on size of container. Label them however it suits you. I even have canned vegetables in a seperate file from frozen, but I also have been collecting coupons a long time, this may not be neccessary for you yet.
Step 2 Start cutting coupons every week, loyaly. All of them. If it is a product you know you will never use, then don't go through the trouble. If it is a product you may use for an Easter dinner only, cut it out. Also, start keeping those grocery store ads. All of them. If you don't recieve them in your mail, pick them up each week when you shop.
Step 3 Now combine your coupons and your coupon container. File them so they are easy to access when you need one. This huge container wont be shopping with you, so make them easy to find. Each week you will get out only the coupons you need for the shopping trip and put them in a small coupon organizer or envelope. (I carry an envelope with my shopping list written on it).
Step 4 Buy alot of what is on sale, when it is on sale.Some weeks you will by alot of vegetables and no meat. Other weeks you will buy alot of cereal and no frozen food. It does work out though. After 2-3 weeks you will have a well stocked kitchen for 1/2 the cost.
For example: We use ground chuck rather than ground beef. This is regularly about 89¢ more per pound than the ground beef in my area at regular price (about $1.89 lb). Every month or two it goes on sale for 99¢ a pound (less than the ground beef). During this time I buy around 20 or 30 pounds. Lets say 20 lbs., this saves me almost $20.00 ($17.80). At 30 lbs. it is a savings of over $25.00 ($26.70). And this still does not include the savings because of less drained fat after cooking. Ground chuck is very lean and high quality. Beef loses much of its weight after cooking because of the fat.
Step 5 Use coupons combined with sales. Most stores allow this, and little do many know, they also let us use one coupon per item even on a buy one get one free sale. Yes, really!
For example, lets buy some Hamburger Helper™. Around here it is about $2.50 per box at regular price ($5.00 for two, of course). The grocer is having a buy one get one free sale. This grocer also doubles all coupons up to 50¢, making them $1.00. We have 2 coupons for 50¢ off any Hamburger Helper™ item. The grocer doubles each of these when we buy one box and get the second free. $2.50-$2.00 in coupons=50¢ for 2 boxes of Hamburger Helper™. 25¢ each! (Fun Huh?)
Another example: Cereal is $4.50 per box at regular price. The sale is two for $7.00. You have one coupon for 50¢ (this will be doubled by grocer to $1.00 off), one coupon for $1.50 off, and a third for 75¢ off (unlikely these would be doubled). Which two coupons should you use? Because coupons are only doubled at 50¢ or less making them $1.00 or less, the 75¢ coupon is worth less than the 50¢ coupon. Use the 50¢ and the $1.50 off coupons. $7.00 - 50¢ doubled to $1.00 = $6.00 - another $1.50 = $4.50 for two boxes of cereal. Basically you just recieved a full box of cereal free!
This grows though...see step 6!
Step 6 Save all rebate information. Include reciepts, proof of purchases, and whatever else the rebate requires. (Please read step 5 if you haven't).
Now lets say this particular cereal company is offering a $2.00 rebate for every 10 boxes of cereal you buy. You have either stocked and bought it all at once, or bought the cereal over time. Because you bought them using the above sale and coupons, you paid $22.50 for all 10 boxes (regular price was $45.00). Now you send in your rebate and get another $2.00 back. $22.50 - $2.00 = $20.50. The cereal was now about $2.00 a box as opposed to $4.50 a box. You have saved more than 50%!
Step 7 Shop more than one store. Find the best deals at each store and take advantage. We have three larger stores here; Walmart™, Kroger™, and IGA™. I usually shop at two per week. Walmart usually has the best prices for toiletries, and Kroger™ usually has the best prices for groceries. I will go to IGA™ if they have more than five items on sale at great prices. (Be aware of IGA™, they usally require at least a $10.00 purchase for sale prices to be effective. In other words don't go to buy a case of cola, you will pay regular price. They also limit how much you can buy of a sale item. Their loss!). Also consider gas and milage when store hopping. I am lucky enough to have all stores somewhat close to each other. Don't drive 20 miles to save 25¢ on a loaf of bread.
Note: Be coupon careful when doing this. Example: Shampoo is $1.75 at Walmart™ and $2.00 at Kroger™. If you have a 50¢ off coupon, where should you buy the shampoo? It would be better at Kroger™ because they will double the coupon, making the shampoo cost $1.00. Walmart™ does not double and the shampoo would cost $1.25.
Step 8 Don't buy just because something is on sale or offers a coupon! If it is a $5.00 item and on sale for 25¢, but rots or sits in the pantry un-eaten, you have not saved $4.75. You have wasted 25¢.
Step 9 Put the word out that you use coupons loyaly. After only a few weeks of using coupons, I started recieving the newspaper inserts from my grandmother and my husbands grandmother. They each use between one and three coupons from each Sunday and the rest are mine. Irregularly, I also recieve the inserts from others.
Step 10 Find people to trade with, such as neighbors and family. I also just found a newsgroup specifically for trading coupons. It is done in any number of ways such as equal values, equal amount, just trading all you don't use not worrying over who gets more or less (this is probably best otherwise coupons expire unused, and for what?), postage stamps, etc. Discuss with the people you trade with what your preferances are and come to an agreement.

Get more information about clipping coupons at About.Com Couponing And Refunding.