Before learning how to cook, you should have a complete set of the most basic cooking equipment in your home. This way, when you see a recipe you like, you can just buy some ingredients and you are good to go.
Basic cooking tools for frying
When deep frying, you need a heavy skillet that is deep enough to contain the oil needed. You also need a frying rack, especially for industrial cooking. If you just need to stir fry foods, a simple frying pan will do. You will also need something to stir or flip what you are frying. One such tool is a spatula. You may also consider using a tong, depending on the food being fried.
Basic cooking tools for steaming
Steaming is a healthier cooking technique than frying. A steam pot is enough for you to start steaming some food.
Basic cooking tools for sauteing
There is a sautee pan, especially made for this cooking technique. It stands straight instead of sloped like a skillet. A sautee pan is about two to three inches high. You will need a cooking equipment to stir your food, as well. You can use a tong or a spatula.
There are many other cooking equipment out there, each of them making every cooking technique much more easier.