Supermarkets / Grocery Shopping
Grocery stores and/or supermarkets are mostly all over the place in the USA. There are national chains and local or regional supermarkets.
Opening hours are flexible, i.e. some are open around the clock, others not. If not, most are opened from ca. 6/7 in the morning until 7/8 in the evening, but mostly longer. The smaller the town or village the sooner the close - that might be a rule-of-thumb.
National holidays are observed more or less - the latter is common. Thanksgiving and December 25th are the 'highest' holidays and you may encounter 'closed signs', at least for a half day, so it's a good idea to have enough food stored.
Whether a supermarket sells alcohol or not, also during which timeframe of the day, depends strongly on the state and even county. A rule-of-thumb is that they usually sell beer up to 3.2 vol % alcohol; they often sell wine, too. Liquor is usually sold in special stores, called "liquor shops". They usually have everything you might want.
That means "buy one get one free" and is a typical marketing slogan for advertised specials. The price you'll see will then (in case it's maked as BOGO) applies to 2 units of the product. Some stores require that you indeed buy 2 units, others will sell you 1 unit for half the price. So better be aware of this technique and ask if unsure.
Large Supermarket Chains
Probably all of the supermarket chains have a pharmacy and a drugstore department which means you can get your prescription drugs or OTC ("over the counter" medicine without prescription) products and personal care products there as well.
Examples for large supermarket chains are: WalMart, Publix, Safeway, Albertsons, Winn Dixie, KashnKarry, etc..