I live in South Florida - the land of expensive groceries and NO double coupons. But I still manage to save quite a bit with coupons (I'd say $10 a week). But it's taken me a while to "learn" the best way to do it.
Before you even start USING coupons, I would plan for 2 weeks to gather coupons. Here's what I would do
1. Every Sunday, get the coupon inserts out of your local paper. There are often ways to get these inserts without subscribing to the paper. There are 2 free weekly local papers that are delivered to my condo complex which have the full Sunday inserts. There are usually 2 inserts: Smart Source and Redplum. I usually get 2 copies of each, if possible. Just cut out the coupons for products you actually use and buy. I usually cut 2 of each coupon.
2. Go to the online coupon printing sites: coupons dot com, Redplum, Smart Source, Coupon Network. These coupons are often DIFFERENT than the paper inserts. Print the coupons that you will actually use. Also go to Target's website and print their coupons - they have tons of great coupons online, and your grocery store may accept them as a competitor's coupon (Publix does).
3. Get familiar with your grocery store's sale ads. What day of the week does the sale switch? Go over the sale flyer and make a list of the items on sale that you either need for your cooking for the week or you could stock up on (cereal, etc).
4. Start reading a good coupon website specific to your grocery store - I recomment I Heart Kroger (google it). She publishes a list every week of all the items in the Kroger sale flyer, and what coupons match up to what items, with links to coupons that you can find online and print. (I use her Publix website to help me). A website like that will also give you links to other sources of online coupons (manufacturer's websites, etc.).
5. Finally, you have to compare prices carefully. Like someone else said, it's easy to think that because you used a coupon, you saved money. I generally won't buy a product with a coupon unless it's something I need, and cheaper than I could get the generic store brand for.
6. Practice matching your coupons to what is on sale in the grocery store sale ad. For example, at Publix here, there's often a few brands of cereal that are buy one, get one free. I have a coupon for $1 off 2 boxes, so that's a good savings for me.
It is time consuming and there is a learning curve. I would recommend just getting comfortable with couponing at your grocery store. Then work up to Walgreens and CVS couponing (they are advanced!

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