I coupon, but not what some would consider "extreme"... but I think planning is more valuable than coupons.
Before you even get into coupons, consider these things:
Think about sales. Just paying attention to what is on sale and that you can freeze (or doesn't spoil) can be huge savings.
Look at per unit prices. There are many things where the larger packages are NOT cheaper (Cereal is a huge guilty party here). People make that assumption, so the marketing/sales people take advantage of it. Also if you buy larger and it spoils, you've lost the benefit. Bigger is not always better.
Pay attention to different prices. "Buy one-get one" at one grocery store may be equivalent to 20% savings at another store. Don't get into "how much did I save" - think - and calculate - "how much did I spend?".
Consider how much time you are willing to trade for money. The folks that do this to extremes can spend a lot of time and get into complicated organization systems. I keep it simple and spend less than an hour a week. There was an "entry cost" during the first few months I did it, as I got fully ramped to all items and documented what is a good deal.
Some other preparatory thoughts:
Figure out what you are buying and where you are willing to compromise. I have not compromised in what I buy. I still get the same brand name products, including flour, butter, etc. as I did before I started using coupons. Keep track of what you have that "turns over" quickly. I eat a LOT of chicken, and stocking up when it's on sale has probably cut my expenses on chicken in half. Some folks are driven by what prices dictate and are flexible on foods. This is 100% a choice.
I have chosen to use online coupons, but not get a paper. The "extreme" folks sometimes have multiple subscriptions to the paper to get multiple copies of coupons. Some of this is learning what coupons tend to be only on paper vs those that are online. Some will be both places, but the paper copy be 25c better or some such. Realize you can usually only print 2 coupons per computer. I have also chosen not to ethically bend that by employing multiple computers. There are also rebate applications (Ibotta and others) that I don't do, again a choice.
Know when the sales turn over at different grocery stores in your area. Is is Saturday/Sunday? or Tuesday/Wednesday? etc.
Figure out where you can go and how much you need to save to make it worth it. I'm single, so the amount of food consumption I experience is small, thus long drives to distant grocery stores for small amounts of stuff don't make financial sense. It's rational to ignore 1 or 2 coupons, especially if they are small and for mediocre deals. Think about your commute as well as where you live. I'm (very) lucky in being able to hit 4 brands of grocery store (6 if you count Target and Walmart) within a <1000 foot detour on my (8 mile) commute. All but one of those are within 1.5 mi of my house if it's a weekend. So I have LOTS of options that make my system work... but even so, it's a rare week I will hit more than 2 stores (and those border on necessary to keep milk stocked in the house :) )
How to find deals:
Use sites like those recommended above, (or southern savers, or living rich with coupons) - find those that serve your area. Get familiar with how they work and how they tag deals. They will often tag what they think are super deals - pay attention to these, but recognize they fall victim to the "how much did I save" mentality in some cases (but they are right most of the time). Learn to skim the sites or go directly to the grocery stores/drug stores on the site. There are a lot of posts on these and it can be a time sink reading everything (remember the time trade).
Recognize that every area is different and deals will be different. The deal you see online may not be in your local store. That's why it's useful to bookmark your local grocery store flyers and skim them. In some cases, they are organized by category and you can quickly hit the 4 categories that matter vs reading through the whole thing. You'll also sometimes see something you missed in the summary sites. I browse these on my phone so I can easily keep the tab open and so I can do it when I'm otherwise stuck (elevator, in line, et al) and can effectively use 1-2 minutes of time.
Recognize different types of stores will likely be better for different types of products. You will have to learn how it works in your area. For me, Rite Aid, CVS, Walgreens et al are great for toothpaste, paper products and the like (generally NOT food). I've found Target to be surprisingly good for things like cleaning supplies and trash bags, if you can line up their "get a $5 gift card" along with a coupon.
On couponing itself:
Learn which local grocery stores double coupons... that can add up in a hurry (and is often the grocery stores with higher base prices).
Start small. Read the ads and know what you are buying today (or have low stock in the house) and if they go on sale and have a decent coupon available as well, use it. Don't try to be perfect on day 1.
Write down what you're buying, and for what price. Keep track of this over time for the most relevant items (where relevant is what you buy often and what goes on sale enough to make it worth it... you will learn this over time). Then look at base prices at different stores so you get a sense of where base prices stand for certain items. I have a running list of just under 50 items in my phone where I know what the "great" price is... (basically the lowest price(s) I've paid w/ the coupon value over the time I've been doing this). I don't expect that list to grow.
Learn that some coupons you print will be good for a set period of time (e.g. good til Aug 15) others will be for one month from day of print. It's a bit of a game in deciding when to print vs when to risk the coupon disappearing. You will learn over time what is best (there are a few brands that disappear quickly, most are pretty persistent)
Once or twice a month fully browse a few coupon sites. (coupons.com, redplum, smartsource are the ones I skim)... this will help you see things that may never have had a match with something on sale at the grocery store.
A reprise on "bigger is not always better": The unit price changes with a coupon. 75c off when the two sizes are $2.50 and $4.50 may make it $1.75 and $3.75 - so if one is double the volume of the other, two coupons on the smaller package is better than one on the larger one.
Expect a month or two of "stock up cost". I had two high $200 months as startup, but now run just over $100 (and that's with meat like Turkey and Chicken in every dinner - things that are generally not cheap calories)
On planning:
I own a foodsaver. It's amazing. I'd advise getting a food scale as well (like a $15 one from Amazon). I can cook food in bulk (e.g. a 21 lb turkey) and freeze it in portions I can use over time (freeze the portion with 1 Tbsp of broth and it won't get freezer burn, and you can just punch a few holes in the bag with a knife before microwaving for a few min on 50% power for nice, fully cooked but still juicy meat...) I know exactly the portion to freeze, so I produce very little waste. I can do the same with chicken breasts, so I get about 1.5 meals per chicken breast... so I'm saving by not wasting. (Of course, it also means no leftovers, so my lunches are all fresh meals)
Consider a chest freezer. I am pondering one, and am currently running through a "model" of when sales occur during the year vs the cost of owning and operating the freezer. I won't know the final answer until November, but it's looking pretty close to a wash right now, so may be useful for a family of 3.
...
Doing this my food cost is down about 35% (admittedly less than half from coupons)... and the quality of food I eat is way up. My "fast food" dinner this evening (ready in 8 minutes) is turkey breast and two ears of fresh corn. Total cost (including the 20c for the foodsaver packaging) is under $1.50.