Inspired by the 'natural living' thread, I thought I would share my experiences with growing my own vegies. I have had the garden for about a year and have had some success and some failure.
Preparation- very important. You need to have soil with lots of organic material (ie compost, manure). I have a raised bed as I didn't want to have to dig up my clay. I've added about 20cm of good soil. You will also need mulch, I find straw is best for the vegetables. I have also got a little fence around mine to deter Ziggy from digging up my plants.
Position- you want a place with at least 4-6 hours of sun a day. In the summer months, I need to put shadecloth over my more sensitive plants, you may have to do this if it gets above 32 where you are. The amount of space you need is determined by what you want to grow, 1.5x1.5 m is a good starting point. My bed is 2x5m.
What to plant?
For a 'beginner' garden, I recommend:
herbs (parsley, basil, thyme, oregano, rosemary, sage, mint). Parsley can manage semi-shade, as can mint. You may want to keep the mint in a pot as it does spread quite a bit.
lettuce- it is so easy to grow. Just ensure that is doesn't get sunburnt, and make sure it gets enough water (easy to tell, will wilt if too dry). You only need to buy one lot of seedlings, because once it gets old enough the lettuce will go to seed. You can replant the seeds for a never-ending supply of lettuce! Really it's so easy, and you can pick a leaf as you need it, so no paying $2 for a lettuce that dies in the fridge after a few days anymore.
tomatoes- I recommend cherry tomatoes, you get fewer pests than with full-size, and they are a bit more forgiving as well. If you are lucky you will get several months worth of fruit off your bush. Six-eight plants is a good amount to start. You may need to add some lime to your soil if you notice the tomatoes looking 'soggy'.
cucumbers- these grow on a trellis. Four plants will give you a good yield, two or so cucumbers a week.
eggplants- I have four plants and I get at least 2 eggplants a week. They are attractive plants and seem quite resilient.
chilli- these can grow in a pot or in the ground. My rainbow chilli has the best yield.
That is a good start.
Some notes on other crops:
pumpkin- usually two pumpkins per vine. The vines take up lots of room, and will spread over a large area if you let them.
carrot, radish, beetroot- these take quite a lot of time to grow, I don't think you could be self-sufficient with these unless you planted quite a large crop.
snowpeas- I grew these last winter and they were sooooo good, 100x better than bought ones. I didn't get a large yield however (having said that I only had two plants).