Trussing a chicken isn't really a "vital" skill per se. But if you spend any time at all around chickens, you'll have to square with the task some day. This applies especially to anyone who claims to know anything about food; say you're anything more than a beginner cook and that you don't know how to tie up a chicken, and people will laugh you right out of the kitchen. In fact, during one of his first jobs Thomas Keller himself had a knife thrown at him by a rather irate chef when he revealed he, despite claims of being a professional cook, could not truss a chicken.
The purpose of tying a chicken up like this before roasting is to help it cook more evenly. The goal here is to hold the chicken together, and make it as ball-like as possible. You don't want bits sticking out, you don't want bits moving around, and you definitely don't want bits falling off. This way, all the parts cook evenly and you don't end up having burnt wings and a raw breast, or overcooked drumsticks but thighs that are still bleeding. To that end, I also stuff the chicken with lemon and some herbs; more details on this in another post. The method of trussing I favor accomplishes the above without any complication and fancy ropework. And more importantly, it's extremely easy to take off after the bird is done roasting and you just want to get the bastard carved and plated already.
For an average 4-pound bird you'll need a piece of butcher's twine about 3 feet long. Any piece of food-safe (i.e., won't melt or burst into flame in the oven... Cotton is probably a good idea) thin twine will work. Don't bother taking out a ruler; for most people, this is the distance from the middle of the chest to the tip of the fingers as they hold their arms out to the side. Use a bit more to be safe. Lay the chicken down with the breast side up. If you're unfamiliar with which part is the breast, consult your nearest chicken manual.
The first thing you'll notice is that the wings are extended out to the side. In the oven, this would leave them very exposed to the hot air, leading them to overcook. To remedy this, the best way is to tuck them under the breast. This brings it close to the body, and makes the rate at which it cooks closer to the rate at which the breast cooks. It's not imperative to tuck them in picture-perfect here; just accomplish the main goal. Also don't be afraid to force it a bit; the joints are stronger than you may think, and the flaps of skin are very easily moved. The worst you'll end up with is a dislocated wing, and let's be honest here: nobody's going to notice anyway.
Next, point the chicken with its neck away from you. Bring your twine under the breast from the front, then back towards you. Tie an overhand knot, above the tailbone. Some people like wrapping up the tail a bit here but I think that's overkill. Bring the twine above the drumsticks, and tie another overhand knot, getting it as tight as possible; again, you want to make the chicken as ball-like as possible, with as few bits sticking out as possible. Tie it off with a second overhand knot.
And now you have a bird, all trussed up and ready to pop into the oven.