Installing a new pendant light can often be just a matter of taking down an old fixture and hanging your new one, and there are two things which help make this project less of a burden: First of all, with the exception of larger chandeliers, which can sometimes be heavy, most pendant lights weigh little enough to be hung from a standard ceiling box. That also means that they aren't difficult to lift and that they can be balanced on top of your stepladder, or temporarily supported from the ceiling box with a home-made wire hook. Second, with the exception of most track lights, pendant lights are hung from a canopy. That gives you the advantage of being able to support the actual fixture "off to the side," on your ladder or on a temporary hook, and have both hands free to make the electrical and mechanical connections.
Removing the Old Light
Before you start removing the old fixture, turn the power to it off at your electrical panel by flipping the circuit breaker or removing the fuse. Yes, the switch on the wall turns the power to the light off and on, but that doesn't mean that turning it off will kill all of the power in the box above the fixture. The power from the panel may come into the ceiling box before it goes to the switch—that's actually the norm in most older houses and apartments—or there may be power going through that box to other loads. Either way, you want to make sure you'll be safe by turning the entire circuit off, not just the part controlled by the switch.
As you take the old fixture down, note how the wires are connected. Mark which wire in the ceiling each of the fixture wires is spliced to. There are three types, or functions, of wire for a ceiling fixture: the ground, the neutral, and the hot wire. The hot wire from the switch is usually black or red, but not always. The neutral wires should be white or gray, and the ground wire should be green, or bare copper. The important thing to note is which wire in the ceiling is connected to the black fixture wire(s) (that's the hot wire from the switch), which wire is connected to the white fixture wire(s) (that's the neutral), and what the old fixture's ground wire is connected to. There may not be a ground wire in the ceiling box if your house or apartment was built before about 1970, but there may still be a ground there. If the ceiling box is metal and the old fixture has a bare wire connected to a screw in the box, that's the ground.
Take the hot wires apart first, then the neutrals. Take the ground wires apart last. Set the old fixture aside. If your new fixture has a mounting plate or strap, attach that to the box next. Lift your new fixture into place. If it's a bit heavy or clumsy to hold up or to balance on your ladder, you should be able to use a piece of coat hanger wire, bent into an "S" shape, to support the fixture while you connect the wires. Connect the ground first, then the neutral, and then the hot wire.
By taking the wires apart, and connecting them back together in this order, you're ensuring that you have two important safety valves in place each time you're working with the ungrounded hot wire. The last one you take apart, and the first one you splice together, is the set of ground wires, also known as the Equipment Grounding Conductor, or EGC. As its name implies, that wire is connected directly to the ground or earth. You can think of it as the emergency overflow drain for the electrical system. The second set of wires you take apart or put back together, the neutral conductors, are the regular drain for the system. The set you take apart first and put together last, the ungrounded conductors, are the supply line. That way, if there's any power present that you overlooked, or if somebody cut it back on after you turned it off, that power has two ways to leave the box without trying to go through you.
Once all of the wires are made up and folded up into the box you can mount your new fixture's canopy to the box or to its mounting strap or plate. Then you can climb down and admire your work. The light bulbs go in last, but you should go wash your hands before doing that step. It will help your bulbs last longer.