The standard ways are:
-boiling: this takes about 20 minutes unless the potatoes are cut small. Skins can be removed before or after (or not at all)
-frying: either shallow-frying in a pan (usually sliced thinly) or deep-frying in a special pan or deep-fat fryer (most chips are cooked by this method)
-roasting: potatoes can be brought to the boil, boiled for 1-2 minutes to soften, then shaken up with a little flour and cooked in hot oil or fat, for 25-30 minutes in the oven at 180 degrees
-sautéing: first boil the potatoes and leave to cool. Then slice thinly or cut into chunks, and cook in oil or butter until golden.
-steaming: healthy and tasty, but surprisingly slow. Allow a good half hour unless potatoes are cut small. Cook in an electric steamer, or a steaming basket over a pan of hot water.
-baking: this can be done in the microwave (about 10 min for a large potato) but the oven gives a crisper skin, especially if you rub it with salt and oil first. In a 170-degree oven they take 30-45 minutes: you can cheat with a quick microwave blast, followed by crisping up in the oven.