Need I say, with great care? For a pot full of hot oil is a dangerous weapon, as the medievals knew well, so please know what you're doing before you embark on a deep fry adventure.
The easiest way to proceed is to buy a deep frier. It always seemed to me to be a superfluous gadget that would just make it way too easy to fry food, but hey, if that's your thing, go for it. Then you just plug the bugger in and fry away.
In Asia, of course, they deep fry in a wok, but I usually use a pot, because I find it better contains the inevitable splatters, and because it has a lid that I can slap on the pot in the unlikely event that the oil bursts into flames. (It could happen, though I've never actually seen it.) Oil fires will go out if you smother them, so it's a good idea to have some kind of cover close by, just in case.
Don't worry, though: you won't have a pot of flames if you proceed with caution.
Obviously, the type of oil that you use is important. I go for a compromise between ease of use, flavour, and affordability, so I usually settle on a clear peanut oil. It's more expensive than your basic vegetable oil, it's true, but cheaper than olive oil, and it's relatively bland - though once I bought peanut oil in Chinatown and it had a strong odour and flavour of peanuts. Won't do that again. I use Mr. Peanut or whatever that stuff is - Planters? Peanut oil is good because you can heat it quite hot and it won't smoke or burn.
Okay, so you need the oil deep, deep enough to immerse your food without touching it the bottom. Quite a lot of oil, in other words. So glug it into your vessel of choice, remembering that the oil will bubble up when you first throw in the food, so don't fill the pot more than about half full. Then you want to turn on the heat; I go for a medium-high. A well-equipped kitchen will have a deep fry thermometer, and you can then easily heat your oil to the optimum 365°F. If you don't have one, though, don't despair. When the oil's hot enough, you'll see swirls forming at the bottom of the pot. I look for that, and then I plunge a wooden chopstick into the oil; bubbles should form all around the submerged stick. Finally, when you think the oil is ready, drop - gently! - a small piece of whatever you'll be frying into the oil; if it rises to the top instantly and gives a cheerful bubble and sizzle, the oil is ready to use.
If the oil is too cold, the food will soak up grease and not form a nice brown crust. Too hot, and the crust will brown before the centre of the food is cooked. Also, don't let the oil smoke; this is a sign that it's too hot, and it'll give your food a burnt taste. So take some care to get it just right.
Fry your food in batches, just enough so that the pieces are not crowded in the pot and can move around easily. Usually you'll need to turn the food over to make sure that it browns on both sides. A good big spider (mesh skimmer or strainer), or a wire frying basket, will serve you well: it will allow you to gently introduce the food into the oil and also easily remove it without bringing a scoop of oil out too. Set the food on paper towels to cool and absorb some of the excess oil. Let the oil reheat briefly before adding the next batch.
Please dispose of your used oil with care. Don't pour it down the drain: our sewage systems have enough to deal with without that. Let the oil cool completely, and then pour it into an empty bottle or jar and throw it away in the garbage. Or give it to McDonald's to use.
Should you re-use your oil? Never more than once or twice, in my opinion, and then only if you are using a similarly flavoured food: don't reuse oil you've fried fish in for doughnuts, say! Please note that though dannye says that thrice-used oil makes the best fries, others say that re-used oil is a carcinogen, particularly if stored for a long time and at room tempearature. Certainly burnt food particles left in oil are carcinogenic, so if you are going to re-use the oil, make sure to filter it well through several layers of cheesecloth to remove any sediment, store it in a cool dry place, and re-use it within a month or two at most.
All in all, though, I think both dannye and I would agree that you should make your own french fries and other deep-fried treats rather than getting them at some fast food joint. Pricy, true, and a little tricky, but much more wonderful.