In a modern car, there isn't a lot of maintenance that has to be done on a regular basis. Fill up with fuel, check your window wiper fluid, and nearly everything else takes care of itself. Except oil changes.
Inside your engine, a series of pistons move up and down rather rapidly. Some cars engines (such as the rather delectable i-VTEC engine in the Honda S2000) can rev up to 9000 rpm, and on each one of those revolutions, all four pistons slide up and down inside their respective cylinders twice. That's 4 cylinders, each doing 18,000 movements per minute.
Even when you are cruising along at a placid speed, you can expect to do around 3,500 revs. If you drive for an hour, that means over a million and a half cylinder movements. The only thing that stops your cylinder (which is made of metal) to scrape against the piston (which is also made of metal), is an incredibly thin layer of engine oil.
When running, the engine oil can get seriously hot, which can cause it to lose some of its characteristics. Seeing how important oil is to cooling, lubrication, and general well-being of your engine... Needless to say, if you want your engine to last, engine oil changes are vital.
Should you change your oil yourself?
No, not really. Thing is, most modern cars need to go for a full service on regular intervals. The garage will check all your fluids (brake fluid, transmission fluid, some cars need hydraulic fluids, etc), your bulbs, your brake pads, brake disks, your wheels, tyres, etc. Whenever it's time for an oil change, it's generally time for a service - either full or partial - and you will probably regret not doing them in the long run.
On the other hand, full services are expensive, and oil changes are cheap, so there's a lot of money to be saved. If you do high mileage, you could save a lot of money by doing every second oil change yourself, for example.
How often do you need to change your oil
Brand new cars need their first oil change after only a few thousand miles - 2,500 is a good idea - because the oil easily becomes contaminated as the engine is running in. After that, once every 8-12K miles is quite normal for most vehicles - check your vehicle documentation.
On higher performance road cars, such as big displacement turbocharged engines, expect an oil change to be required every 6-8K miles. Cars that are frequently taken on track, or that are driven hard on the road, more often - Every 2-5K miles is quite normal. Cars that are used exclusively for racing generally get an oil change after every race.
As your car gets older, shorter intervals between oil changes are a good idea, and if you run a vintage car, even shorter intervals. As a rule of the thumb, if you are unsure, do oil changes more often than the manufacturer recommends.
What type of oil should you use?
"Motor oil is a crude oil product. It's refined out of the same stuff that makes gasoline, nylon clothing, and CD parts." - It contains additives, you have to know about oil levels, you need to know the viscosity of your required oil, and the rating and classifications of oils. In addition, you need to make a choice between fully synthetic oils (good for nearly new and performance engines), part-synthetic oils, mineral oils, etc. Of course, I would rattle on about all this loveliness, but the write-up by Bitriot under Motor Oil covers all this ground very well, so go there and read it!
What do you need to change your oil?
It's pretty damn easy, actually. You need the following:
You need to know how big your oil sump capacity is. This will be in your manufacturer's handbook for the car.
A receptacle known as an oil pan, which is basically a big flat container which will fit under your car. This oil pan will have to be bigger than the oil sump capacity of your car.
You'll need a new oil filter to fit your car - any good autoparts shop should be able to help you out here.
You may need a filter wrench - basically a big metal strap that you can tighten around the filter to loosen or tighten it. Mostly, though, you should be able to get the filter off by hand.
You need enough oil to fill your whole oil sump. Be aware that there may be a lot more oil needed than you might think - this can be anything from 4 to 8 litres on normal passenger cars. Big block engines take more, and diesels generally take more oil too.
A pair of plastic gloves would be handy, too. This is dirty work.
Finally, you will need a wrench to take your sump plug off your oil sump.
Starting the oil change
Now, we are ready to actually do the oil change. Park your car in such a manner that your oil sump plug is the lowest part of your oil sump. This means parking it on an incline. This is to make sure that most of your oil will come out of the engine properly.
Put on your plastic gloves. Oil is nasty stuff. Now, locate your oil filter and your sump plug. Many people recommend running your engine for a while before doing an oil change, because the oil becomes less viscous, and can then be drained out of the oil sump more easily. On the other hand, hot engine oil can be a hazard, especially if you've never done an oil change before. Up to you, personally I usually do oil changes to a cold engine.
Put your receptacle under the oil sump, and take off the oil sump plug. Ideally, you'll want to catch the plug as it comes off, but if that doesn’t work, then don't worry about it. Just leave it where it is, especially if you are working on a warm engine (a pair of tongs will come in handy to fish the sump plug out of warm oil!). Be aware that there will be a bit of pressure behind the oil, so it may come out in an arc - be prepared to adjust the receptacle accordingly. Try not to spill any oil. either!
Go grab a beer or something, it will take quite a while to get all the engine oil out, more so if the engine oil is thick and slow-running. You won't want to do anything until all the oil is completely drained out of your engine.
Once the oil is completely drained out, loosen the oil filter, and empty it out into the oil receptacle as well. Bag up the filter, and put it to the side.
Take your new oil filter, and put some new engine oil inside it. Swirl it about to coat the filter. Then, make sure to put oil on the rubber sealing ring and on the threads. If you fail to get a good seal between the filter and the engine, Bad Things will happen - it may cause leaks, and it will make it extremely tricky to get the filter off the car, the next time you do an oil change.
Put the oil filter tightly on the car - hand-tightened plus about a quarter turn is perfect.
Now, check the oil sump plug for damage, and check the seal, if there is one. If the sump plug threads or the plug itself is damaged, you'll need a new one. If it's ok, tightly fasten it back on the oil sump.
Time to fill 'er back up! Pour the manufacturer recommended amount of oil - minus 0.5 litres - into the engine. Then check your dip-stick. Keep filling it and checking constantly until you are reading 'full'. It's important to not over- or under-fill your engine oil.
Now, just start the car and leave it running for a couple of minutes. Check if you can see any oil leaking out of the sump or filter.
After a couple of miles of driving, check your sump nut and the filter, to see if any oil is leaking. If it is, tighten the leaking bit, and keep checking. If you are losing a lot of oil, go see a garage.
How to dispose of old oil
Engine oil is seriously filthy stuff, and pouring it down a drain is not a Done Thing. It's terrible on the environment, and highly illegal as well. Most local garages will take your old oil for free or against a small fee, or take it directly to an oil recovery facility, where they can clean and recycle old oil into other products, including some plastics etc.