Fabric that is exposed to an agitating process, like a washing machine, is coerced to relax into its natural state, causing the fibers to curl up slightly and shrinking the material. A washing machine is the best way to agitate a cotton piece enough for it to shrink, but frequent wearings of a cotton garment will eventually cause a similar shrinkage.
Heat also causes cotton fibers to recoil, or relax, back into their natural state. A washing machine can easily shrink cotton by using the heat from hot water. Exposing cotton to other sources of heat, like frequently wearing a shirt in the sun, can eventually have the same effect as washing a cotton shirt in hot water.
A dryer can shrink cotton without washing the item first. Remove all price tags and other pieces of plastic or paper from the cotton garment or item and run it through the dryer on a high setting. The heat will relax the fabric, causing it to contract and shrink.
Cotton can be placed in a bowl of hot water to help the shrinking process. The problem with this tactic, though, is that the temperature of the water must remain high, which can be difficult to maintain without using a washing machine. Heating water in a tea kettle and pouring it over the garment to saturate it, then adding more as the water cools, can help shrink a piece of cotton.