Shrinking a pure cotton T-shirt is relatively easy. It seems that after each wash the shirt will get smaller and smaller, even if you don't try to shrink it. Shrinking a blended shirt is a bit different. Polyester is added to cotton so that it doesn't shrink much, and the higher the added polyester, the less the T-shirt is apt to shrink. Any T-shirt containing cotton will shrink a bit; the blend of other materials is the key to how much it will.
Wash the T-shirt in the hottest cycle that your washing machine allows.
Dry the T-shirt on the highest heat setting, then wash it again the same way.
Pull it out of the washer and dry it by ironing the shirt with the iron on high.
Boil the T-shirt on top of your stove in a suitable pot filled with water. If possible, put it in a pressure cooker instead, and allow the temperature to reach well past the boiling point of 100 degrees C.
Dry the shirt with the iron; it will have shrunk.
Boiling the T-shirt in a pot on the stove or putting the shirt in the pressure cooker might ruin it, so only use either of those ideas as a last resort. And be careful when using boiling water in either of these two applications to prevent scalding or burning your skin.