Cooking is the skill associated with making food. Successes are gained by successfully cooking Food. Double successes are earned when cooking anything level 2 or above.
You need to be near some sort of fire in order in order to cook. You can create fire yourself by dropping a Bundle of Kindling on the ground. You can also cook on fires found in buildings such as a Forge.
To level Cooking the fastest, you have to cook anything that requires Cooking level 2 or above, as you will get double successes. The cheapest and easiest way to gain maximum successes is to cook Steaks, as they only require level 2 Cooking and cost 1 gp each to make.
Assigning the Cooking skill to a hotkey is very helpful in battle. When you attempt to use the Cooking skill, your hands will automatically be freed. This will let you quaff potions faster (and /or cast spells) when you are in danger. Doing this won't open up the Cooking window either (unless facing /standing-over a fire), so it is the quickest way to drink potions while fighting.