Firstly, you will need the following:
* Socket set (including extension arm)
* Oil pan
* Oil filter wrench (see pic below)
* Z9 oil filter (just ask for a filter to suit your EA-EL six/V8)
* Oil (5L for V8, 5.5L for the six).
* Jack (scissor or trolley, doesn't matter)
* Axle stands (for piece of mind, I wouldn't want to get under a car held up solely by a jack)
^^^ Typical oil filter wrench found on ebay for <$20 + postage ^^^
What oil you decide upon depends on what your budget, what kind of motor you've got (high-km slapper or freshly rebuilt performance motor), or whatever you're happy with putting in your falcon. In my case for my EF (high-km slapper), I bought a 6L cheap-ish bottle of 20w/50 mineral oil. Same deal with filters, I got a cheap Ryco filter.
Heavier oil (15w/40 up to 25w/60) will suit older engines that are stock-ish and may experience lifter ticking, blowby, or are simply used as a daily. If you're running 15w/40 oil and your lifters are ticking, you may find that replacing with 20w/50 or heavier will get rid of the ticking.
Ligher oil (say, 5w/30 to 15w/40) suits freshly-built tight-tolerance performance motors, the lighter weight allows for smoother & higher revving (or more time spent in the higher rpm range).
Synthetic oil is better,particularly if you have a performance motor but you pay a price for it. Also, you can get away with longer periods between oil changes (although this isn't recommended

Anyway enough about oils. On with the oil change!
1)
Firstly, ALLOW YOUR ENGINE TO COOL DOWN BEFORE STARTING. The last thing you want to do is burn your fingers or get hot oil on your face/arm/etc.
2)
Jack car up from the front (with trolley jack, on k-frame) or the jacking points on the sides (scissor jack) and place axle stands under the chassis rails close to the front.
3)
Place oil pan under sump, undo sump plug. This nut requires a 19mm socket. Lefty-loosey righty-tighty applies here

4)
If you poke your head under the car in front of the passenger wheel, you'll see your oil filter through a hole/gap in the chassis, above the k-frame. (If you look from above, it's under the front of your intake manifold). Fit your oil filter wrench to your extension arm, fit that to your ratchet, and slip over the filter from through this hole/gap. Once you start to undo/turn the ratchet+wrench, the wrench will self-tighten around the filter. Remember lefty-loosey righty-tighty.
5)
With your new oil filter, dip your finger into your new oil a few times and apply oil around the edge of the oil filter. This is so it will seal properly when screwed back on. Redo by hand until it seals, and then tighten it up a bit past that point. It doesn't need to be on uber tight. Also, it might take several tries to get it to screw in at first.
6)
Screw sump-plug back in by hand until finger tight, and then with the 19mm socket + ratchet continue until tight (should hardly turn much after finger-tight anyway). Don't go crazy here with brute force or you might cross-thread (or round) the plug.
7)
Remove oil pan & other stuff (old filter, etc) from under car, lower back to ground. Fill with oil through the oil cap on the rocker cover. Remember 5.5L for the sixes, 5L for the V8.
8)
Start car, let it idle for a bit, check underneath for any leaks (if you're unsure about your sump plug or oil filter). Assuming everything's OK, you're right to go!
9)
Use old oil for skids in your residential street, nearby schoolzone, for for laughs at the nearest busy intersection.
Now, assuming you've already got a jack, stands, something to drain the oil into (ie a pan), etc, you could do an oil change on your car for <$30 (cost of cheap oil and filter). If you go for high-performance products (ie decent oil filter + synthetic oil) you may be spending up to $100. If my car wasn't a beater & had a decent engine, I'd probably put semi-synthetic oil in it as a minimum. The "extra" cost of semi/full synthetic oil (and a performance filter) is definitely worth the potential tens of thousands of extra kms (and better performance) you can get out of your motor by looking after it properly.
Excluding waiting for the engine to cool, this should take 15-20 mins tops from scratch, with 1/2 of that time being draining/filling the oil
