So right, this simple thing is reading store flyers. Most neighborhoods in nyc get a weekly sales flier packet dropped off on your doorstep. Bring that in. Leaf through and pull out the ads for the stores you regular shop at/are in your neighborhood. Now go through those ads.
In the drugstore ads: Don't fall for the 2-for-1 on cover girl if you hardly ever wear make-up. Do look for stuff you actually use. I usually keep an eye out for sales on Cetaphil, (the $12 a bottle gentle skin lotion I use) and the brand of toilet paper I'm currently into (used to be Scott, now I look for recycled), and oddly drugstores sometimes run deals on cereal and beer.
In the grocery store ads, the same rule follows. If you drink Chock Full of Nuts, keep and eye out, once a month it goes on sale for $1.99 a can.
Looking through the ads for a few minutes every week gives you a familiarity with prices in your area, so when you see things in the store you know whether or not you are getting a good deal.
Oh, and I don't have a member card at any store. They freak me out. In the discount vs paranoia scale the paranoia wins out this time.
Also, check the date at the top of the flier to see when the prices start, it's usually 2 days after you get the flier. Make a list, and don't shop hungry.