Getting to Australia is definitely not cheap and you do need to save up a little before you even consider applying for the visa. You have to have money for the visa, plane tickets, travel insurance, accommodation, food etc. Even if you hear people saying they went to Australia with no money and managed just fine it might not be the case for everyone.
Proof of Funds
When entering Australia you may also be asked to show that you have enough funds for the initial stay (around 5000 AUD) so it could be a good idea to get a bank statement from your home bank to show you have that money (even if it's not yours and you just asked your parents and friends to transfer it to you account). Having a credit card or two can also help prove that you have the money. In most cases, however, this will not be checked but it's always better to be prepared.
Plane tickets
One-way tickets to Australia can cost up to 1500 AUD so it's important to shop around and look for good deals and when possible book ahead 4-5 months. Of course the easiest way is to go to a travel agent and let them find you the best possible and cheapest route and sometimes they can offer you some pretty good deals. Another way, if you're good at surfing the internet, is to plan and book the trip on your own. This can be time consuming but can sometimes give you the biggest savings. Doing it yourself it's important to make sure you have enough time between the flights because if you miss one flight your entire trip may end up a disaster and you may have to pay enormous sums to get to your destination.
I flew to Australia from Estonia in October 2009 and booked ahead 3-4 months. The cost was 550 AUD in total:
Tallinn - London (Estonian Air) - ca 100 AUD
London - Kuala Lumpur (Air Asia) - ca 300 AUD
London - Kuala Lumpur (Air Asia) - ca 300 AUD
Kuala Lumpur - Melbourne (Air Asia) - ca 150 AUD
Travel and Medical Insurance
Especially when using different flight companies or booking the trip on your own travel insurance is essential in case you miss a flight or a flight is delayed and you miss your connecting flight. Many flight companies will ask you to buy a new ticket if you have missed a flight so having insurance will ensure that you'll get that money back. However it is very important you read through the conditions of your travel insurance and make sure the will compensate for missed flights.
Medical Insurance is equally important for the entire stay in Australia because medical aid in Australia is not cheap. Calling an ambulance will already cost you a few hundred dollars, a regular doctors visit ca 80-120 AUD and more serious cases even more so getting medical insurance for around 500 dollars a year is definitely worth it (price may vary depending the county you're from and the insurance company you use). Medical insurance is usually only available while you're still in your home country so make sure you get it before you leave for Australia.
Some useful links:
Air Asia - Cheap flights from France or UK to Asia and from Asia to Australia
Estonian Air - Cheap flights around Europe
QBE Insurance - Australian Insurance Company that has offices around the world.