Wheat pennies were made between 1909 and 1958, and they vary in worth. Most created before 1942 were made of almost pure copper, and can be cleaned just as any copper or copper alloy item. Before you clean them, consider having the pennies appraised by a coin expert to see how much they are worth and to make sure that cleaning will not diminish their value. Cleaning these pennies is not difficult, nor must you buy expensive products to do so. You do need to be careful what you use, however, or the penny will look worse than when you started; only use cleaners that are recommended for copper--either homemade or store-bought.
Pour 1/4 cup of white vinegar into a glass bowl.
Add 1 tsp. of table salt to the vinegar. Stir the mixture with a spoon until the salt dissolves.
Place a few tarnished pennies into the bowl. The solution will work better if the pennies are spaced out and not crowded--so don't put in too many at once.
Allow the pennies to soak in the solution for at least half an hour. Some lightly-tarnished pennies will be bright and clean by this point; heavily-tarnished pennies will need to soak for an hour.
Rinse the pennies off under clean water. Dry and polish them with a soft polishing cloth. Dry the pennies thoroughly or they will tarnish again quickly.