By far the safest way to deep-fry, is with a deep fat fryer. However a saucepan or wok can work just as well. The secret is in the type of oil used, and getting it to the optimum temperature.
Oils with a high burning point are ideal for deep frying - vegetable oils such as sunflour oil are perfect, whilst you should steer clear of butter and olive oils as these burn at low teperatures.
It is most important when deep frying to check that the oil is at the optimum temperature for even browning, as close to 365 degrees F (185 degrees C) as possible.
The oil should be of a depth to totally immerse the items of food you are wanting to fry. To test the heat of the oil you can use a cooking thermometer or fry a cube of bread. If you pop in a small cube of bread, it should have turned an even, golden brown colour after one minute of frying. It should also bubble when immersed in the oil. This will signify that it is at the right temperature. If it cooks too quickly lower the heat and if it browns too slowly, increase the heat.
It goes without saying, be extremely careful when handling oil at this temperature and treat this cooking method with caution!