Pan Frying is a probably the most the used technique in home cooking. What it consists of is frying food in a pan on high heat with little oil. Things that can be done with pan frying would be cooking chicken breast, sausage, eggs, bacon, etc… This technique is excellent for browning food and then following it up with a deglaze to improve flavor.
Deep Frying is a submersion of food into oil at high heat. If done properly, food would not be greasy as the moisture in the food will repel it. It is a great method for cooking quickly and providing crispy texture. Some deep fried food would be potato chips, tempura chicken, corn dogs and calamari.
Shallow Frying is a method where food is partially submerged in oil, around half way. This method should be used when oil needs to be conserved. When shallow frying, usually the food would be cooked halfway on one side and then flipped. This method should be used with caution as burning of food is a lot easier due to the direct heat from the pan.
Stir Frying is a technique where foods are placed in a very hot wok or pan in a small amount of oil and stirred constantly. This is a great technique to produce a variety of Chinese food quickly and efficiently. Wok should be avoided if you are using an electric stove as the heat from the electric stove is not hot enough.
Sweating is a technique very similar to stir frying but is done on low heat. This technique is primarily used to sweat the moisture out of vegetables to increase flavors.