Self-catering
Large supermarkets such as Tesco and Carrefour exist in most towns, and have a reasonable range of produce, though as this is not an expensive country you should be able to afford to go to corner shops and local supermarkets. A good selection of bread, meat (particularly sausage of various kinds), pierogi (a kind of pasta parcel containing cheese and potato, or some kind of meat) and dried goods such as pasta is available. In some areas of the country fish of various kinds are popular. Fresh fruit and vegetables are a little seasonal, and can be pretty expensive out of season. Often the cheapest way thing to buy is frozen or pickled vegetables such as spinach and gherkins, with potatoes and onions.
Cheap eats
If you try, you can spend a fortune in Warsaw on food. If you are in smaller towns, or you shop around a little though, you should be able to find something in your price range. Kebab shops prevail all over the country, and while these vary in price, they are generally pretty cheap. In addition canteen-style restaurants can be found in most towns, where you can pick foods like casseroles and salads, which are sold by weight. You should be able to get a decent portion of something interesting with cheese and bread for a good price.
Restaurants
Most Polish restaurants are either based around one or another ethnic theme, such as Chinese or Italian, or offer a combination of traditional Polish food and various other options. Polish food will include delicacies such as pierogi and cutlets of meat served with potato and some form of salad. Other options will include things like pasta dishes. Vegetarian options are often a little more limited.
The expensive restaurants in Warsaw thrive on American-style tips - serving staff are otherwise paid a pittance, and may well effectively have money stolen from them by unsrupulous management. Outside of this bubble, a small amount (less than 10%), or rounding up the change is an acceptable tip for a meal. Over-generous tipping is a disease which benefits nobody - don't let it spread!
Drinks
Beer.
Polish beer may all be brewed by large multinational companies (Zywiec, the largest brand is owned by Carlsberg), but they are still brewed in the country, and to much the same quality as German and Czech beers. There seems to be less dark beers and other interesting variants unfortunately, and the gap there is being filled by the usual international rubbish like Guiness. Overall though you will get a half litre of fairly decent lager for between 3 and 8 zloty (ie. between extremely cheap and just fairly cheap compared to Western Europe). In the winter it is often possible to buy warm beer, which is basically just normal lager spiced and warmed up like mulled wine - definately an acquired taste.
Wine.
Don't. Not in bars anyway. You will most likely get a tiny glass of cheap bulgarian plonk which has been open next to the radiator for a month. This doesn't apply to whole bottles or reasonable restaurants of course, but even there wine is hardly a Polish obsession so the range could be a little limited.
Coffee.
The cheapest coffee served in cafes and bars in Poland is usually "turkish-style" - ie. the grains are in the cup, and the stuff shouldn't be drunk until they have had a few minutes to settle to the bottom. Sadly the premium option is often Nescafe (signs are proudly put outside cafes
advertising this). Most towns will have proper coffee shops serving espresso-style coffee (sometimes "in paper cups, New York style" which is by all accounts "now very fashionable"). Suprisingly McDonalds in Poland serve espresso-style coffee, which means that if you just want filter coffee you are totally out of luck.
Vodka and other spirits.
Poland is famous for its vodka, and most places will serve a range of different vodkas, and often vodka-based cocktails. Prices range from dirt cheap to reassuringly expensive, with the average being well below what you would pay in western Europe. You do get what you pay for however, and some of the cheapest brands are probably not even fit for stripping paint. Imported spirits are quite expensive, and Polish-distilled whisky for example is not going to win any awards in the near future, so try developing a taste for vodka.