I can't tell you how easy this project is. Seriously, my bloodhound could do it. This is also one of those things you can do to make yourself happy as a renter, but that won't piss your landlord off. After removing it, just keep the old light and put it back up before you move out.
First, you'll be removing the old fixture - check out our step-by-step instructions:
• How To Remove a Light Fixture
Now, on to installing the new one...
What You Need:
Materials
• New light fixture, including mounting bracket and screws
• Wire Nuts
Tools
• Wire stripper, or a basic utility knife
• Screwdriver or power drill
Instructions:
1. Turn off the circuit breaker associated with your light. I operate on the paranoid end of the fear scale when it comes to electricity, so don't mess with me on this. If you're not sure which breaker operates that particular light fixture, do this project during the daylight and turn the main breaker off. Or get comfortable with a headlamp.

2. Examine your new light fixture and read any instructions that come with it. Every light fixture is different.

There should be at least two wires coming out of the fixture: a white (neutral) wire and a black (hot) wire. In this case, the two were conjoined and covered with protective plastic. Although they look identical, one wire has a ridge that you can feel with your finger. This is the white wire.

3. Separate the wires a little ways, then use the wire stripper to expose roughly an inch of bare wire on each end. If you don't have a wire stripper, gently cut the plastic all around the wire with a knife, then strip it off manually.

4. Next, attach the wires protruding from the ceiling box to the wires on your light fixture. Notice that the ceiling has a black and a white wire as well. The third copper colored wire is the ground wire.

Twist the exposed parts of the white wires together clockwise, then screw the wire nut onto the ends. Do the same with the black ones. Note: you might need help holding the light fixture up while you do this step. The ground wire just hangs out like an awkward third wheel. As long as it has a wire nut, you can ignore it.

5. Tuck all the wires neatly into the ceiling box, then screw the fixture's mounting bracket into the ceiling box, according to the instructions. Once you test it out and see it's working properly, you are done!
Variations That Might Trip You Up
• Sometimes wires from the ceiling box attach directly to the metal part of the ceiling light, instead of to corresponding wires. If so, wrap the black wire around the brass screw, and the white around the silver screw.
• The ground wire is sometimes green instead of copper.
• If there is a green screw on the mounting bracket of the light fixture, loop the exposed part of the ground wire around the screw, then tighten it into place.
• If there is a grounding wire on your light fixture as well, attach the two grounds together and secure with a wire nut, just like you do with the black and white wires.
• In the case of multi-light fixtures, there can be more than one black and white wires. If so, attach all the black together and all the whites together.
HELPFUL LINK:
• How To Remove a Light Fixture
(Images: Dabney Frake)

Commercial Flour Sa...
My heart skipped a beat when I saw this post but I have a dual problem--several ugly old light fixtures that are almost all on pull chains (yup, old apartment). Any ideas? The cost to rewire is several hundred dollars per room so for now I'm stuck...right?
A wire nut on a bare copper wire serves no purpose at all. That wire, which is the ground wire, must be bonded to the metal box, if present, or a ground terminal on the metal fixture bar. If the light fixture has a ground wire, it must also be spliced to that. Be aware that you will be creating a fire hazard if you leave a loose splice behind (a common mistake for do-it-yourselfers).
I live in argentina and don't have a third copper wire. Is that a problem?
DINAHPINAH: Thank you for your comment. I've always heard how 'easy' it is to change a light fixture but honestly, electricity scares me so I hire an electrican..regardless of the cost. What would a fire cost me?! I say, better safe than sorry.
Never have the nerve. The wiring in the house we rent it very old and scary. I would rather live with the ugly lights or have an electrician do it if one goes. Maybe if I lived in a brand new house?! I've rewired plenty of lamps in my time and it does look easy.
Buonpane, we have a 100 year old house with the same issue. If you can't find the pendant you want with a pull chain, I recommend using this pull chain insert.
http://ak.buy.com/PI/0/1000/226149642.jpg
I replaced my first electrical fixture a week ago. It was just a simple closet fixture (the existing fixture was burning out bulbs). I was super excited to successfully complete this project, and it really was pretty simple. It gave me a lot of confidence in my fix-it skills, but I still know my limitations. I'm having an electrician come in to look at my ugly buggy florescent fixtures in my bathroom. Ugh.
love the new light. Do you have a link to where it can be found?
I've rewired a house top to bottom. I'm blessed to have had the opportunity to learn things such as electrical and plumbing throughout my years. I do my best to pass what I've learned to anybody who will let me so they too will be comfortable and confident handling projects such as this. @house voyeur the missing ground wire won't be a problem in your light fixture.
@Tanni I believe the new light is a Fly Suspension by Kartell: http://www.lumens.com/FLY-Suspension-Lamp-by-Kartell/PAAAIAKCKLBHMGDB/product
@buonpane :this should do the trick. However, if you use more than one in a close space, you might end up with mixed signals. http://www.amazon.com/Heath-Zenith-BL-6138-WH-Solutions-Wireless/dp/B001B5QZSO/ref=sr_1_9?ie=UTF8&qid=1346190750&sr=8-9&keywords=remote+light+switch
I have replaced a fixture in my house, but the wiring is very old. I felt better having my electrician come in and do the rest. He had a lot of cleaning up to do. If you have newer wiring, it's a snap.
I purchased two fan/light combos for my apartment and begged my dad to help me install them (having done nothing electrical before, I was a bit leery of electrocuting myself). Dad showed me how to do the first one and I took the lead on the second. It was wonderfully simple. I'm sure there are tutorials on YouTube for anyone without a Mr. or Ms. Fix It to rely on for help.
I bought two LED tubes from www.meteorelectrical.com for my kitchen and found this site simply outstanding to help me fit and install them :)