The public system isn't amazing like Melbourne's, but it is still pretty damn nice (much better than Hobart's!).
I have never driven in Perth but have spent a lot of time there, and the buses / trains have always been enough to get me around.
All public transport services over there are through Transperth (http://www.transperth.wa.gov.au/).
If you can, find a place to stay near a train station, it will make things a bit easier :). about 8 years ago
Perth doesn't have trams like Melbourne but if where you live and where you want to go are near the rail lines then it's quite easy to get around all week.
Trains usually run every 15 to 20 minutes and they are quick and clean.
If you are heading into Perth from the suburbs or around Perth you'll have no problems.
Buses are not so good. They don't run as regularly maybe every 45 minutes during the week and longer on the weekend. If you want to get across suburbs you quite often have to catch several buses.
There is a free-transit area around Perth that covers the City centre and several kilometres out and you can catch a CAT bus or train for free.
The Transperth website has information regarding public transport for Perth. You can use it to plan trips by bus or train around Perth and suburbs.
Its address is www.transperth.wa.gov.au/Default.aspx about 8 years ago