Always thought the only way to jack up the car was using the 4 jacking points (as per Fox's Pic) but actually there are lots of points on both the sub-frame and even parts of the suspension components, the key thing is to understand what is stuctural (a bit of a diffcult thing to convey without pictures, sorry!) but if something looks like a hefty steel 'beam' under the car it's probably safe to have an axel stand here.
Working underneath the car can be a bit tricky without an inspection pit or a lift and you may find, if you have basic jacks, that they don't really provide the required amount of lift to give you enough clearance to work .
If you have a friend or family e.t.c that have experince of working on cars, get them in, even just to help with the jacking process.
A couple of things I use are;
-Handbrake on
-In Gear
-If only jacking up front or back, choc wheels with either shop bought chocs or timber blocks of a suitable size pushed hard into the tyre/ground meeting
-there is a large steel 'tube' (LCA??) at the rears that basically runs from the front of the rear arch to the wheel hub, this basically supports the weight of the car in this quarter and can be supported by axle stands, kind of gets them a bit out of the way too to help with working.
-always jack up as evenly as possible, I have 2 jacks to allow me to do this, one side a bit, next side a bit e.t.c
-to get the extra height (if your jacks are running out of lift and your axel stand adjustments are too big increments) there is no problem in using a LARGE, WIDE peice of SOLID timber underneath them to give them the required boost.
-try to avoid working on a surface that is anything but almost perfectly level, my driveway has a very low gradient, but even with this it can really affect how the car behaves when lifting it.
-Removed wheels placed under jacking points or other areas where you're not working
-before getting under the car I like to give it a good shove (rugby scrum style) from the sides and front and back, it should'nt really move at all!
Just be really careful tho, this is probabaly the most dangerous thing that you can do with your car and I would imagine a ton of steel on a squidgy human body is gonna be an issue when you've got 12HR waiting times in A&E.
I'm fairly new to the whole 'working on cars', if i'd known what I know now I would have bought a 2T trolley jack