As is true for most culinary tasks, deep frying can be accomplished with a wide variety of equipment. You can buy a dedicated deep fryer, but that isn't necessary. In fact, if you're new to frying, it's probably best to start out simple.
There are a few pieces of equipment you'll need, but chances are you've already got them in your kitchen. What you don't already have shouldn't be too pricey or hard to find.
Equipment for Deep Frying
Here's what you'll need to become a pro fry cook.
Heavy, Deep Pot
Find a heavy, relatively deep pot with a capacity of four to six quarts. For example, a 5.5-quart enameled cast iron pot will do just fine. While cast iron isn't essential, it does hold heat well, which is a plus when deep frying. The light enamel interior makes it easier to see what you're frying, so you'll less likely to overcook your food, but uncoated cast iron will work if you're careful.
The larger the pot, the more oil you'll need, but the upside is that with more oil, the temperature will be more stable and will recover more quickly. In any case, the pot should be deep enough to hold about three inches of oil (at least) with another three inches space between the top of the oil and the top of the pan.
Use a thermometer that can accurately register from 350 up to 400 degrees. Granted, you should rarely let your oil get that hot, but that's the range you'll be working in.
Deep-fry thermometers usually clip to the side of the pot, which is handy, but a probe thermometer will work too.
Spider or Skimmer
A small "spider" or skimmer is useful for removing cooked food. A spider is a wok tool with a wooden handle and a wire mesh basket. They come in several sizes; regular sized spiders may be too large for many pots, so check the dimensions before you buy one.
The other option is a skimmer, which is designed to skim foam from stock and is generally smaller than a spider, with a flatter basket with tighter mesh. The looser mesh of a spider leaves more of the oil behind, making it easier to drain your food. As long as a spider will fit in your pot, it's a slightly better choice.
While not essential, a splatter screen is helpful in keeping the mess to a minimum. Some newer models contain filters designed to help reduce frying odors as well.
Rack and Sheet Pan
A rack placed over a sheet pan is used for draining fried food. While you can use a plate or pan lined with paper towels for draining, they can result in soggy or greasy food if used improperly. Plus, if you want to be able to keep a batch of fried food crisp while you finish a second batch, you'll definitely want a rack and pan. You can find sets or buy them separately; the racks are often sold as cooling racks for baked goods.
Deep Frying Using an Electric Fryer
If you do a lot of deep frying, you may want to consider a dedicated fryer. Electric deep fryers are available in several sizes and price ranges. They all have the distinct advantage of reducing the mess of deep frying; vented lids almost completely eliminate splattering and many units have filters that help reduce (but don't entirely eliminate) odors from frying.
A few fryers have the capability of filtering oil for reuse, which is a very helpful feature.
The downside for some fryers is the temperature control; the upper limit for most deep fryers is 375F, which is adequate if the oil actually reaches that temperature. In my experience, though, the real temperature can vary as much as 10 or 15 degrees from the setting on some units. Keep that in mind as you read reviews; with a little research, you should be able to find out which units are best at temperature control. Another factor to consider is the size; a small unit (1-2 liters of oil) will take up less space but even if you're just cooking for two, it may require frying multiple batches.
Oil for Deep Frying
You can deep fry with a pretty wide variety of oils. Your main concern is what's called the smoke point, which (unsurprisingly) is the temperature at which an oil starts to smoke.
You don't want that to happen. Not only is it potentially dangerous, but there's some evidence that being heated past the smoke point releases free radicals in oil, which may be linked to some kinds of cancer.
To be on the safe side with deep frying, use an oil with a smoke point of 400F or above. Fortunately, there are quite a few oils that fit that criterion. (Here's a chart listing the smoke points for most cooking fats and oils.
Refined peanut oil is a popular choice for deep frying, as are safflower, vegetable and canola oils.
Unrefined oils of any origin are not suitable for deep frying. They simply have too low a smoke point, and because these oils tend to be very expensive, they're not practical anyway. Keep in mind that many oils are sold in both refined and unrefined versions. If you're buying an oil for deep frying, make sure you buy the refined type.