Atillia, if you go to any half decent ISP that provides webspace, they will do it for you and look after reminding you whenthe domain name falls due for renewal every two years.
You could go direct to a domain name seller like
www.melbourneit.com.au but its generally cheaper and less hassle to go through a re-seller.
Another quick word of advice. Most people want to register a domain name becaue they have thought a beaut and catchy website address. You may type this address in and find that its not listed. But that that doesnt mean it hasnt already been taken. People often register domain names and never bother with putting up a website.
You should go to a 'whois' site to find out if your name is taken.
www.melbourneit.com.au have a whois section and will let you know if the name is available or not.