You cook it for about half an hour - of course this depends on the size of the beetroot. Leave at least an inch of stem on to stop it bleeding so much and put some salt in a pan with the beet and cover and bring to boil, lower to simmer and cook until soft. Drain, allow to cool and the skin will just rub off.
You don't cook it, you roast it!
Actually you can cook it too, but it tastes a lot better when roasted.
Leave on some of the stem - about an inch and snip away the root. Boil with some vinegar for about 20 to 30 minutes until they are soft. You can wrap them in foil and bake them in the oven.