Here in Australia, you can legally change your own light bulbs and operate all of your appliances as long as you are using them in a way they were designed to operate. For any electrical work that goes beyond those parameters, you are required to hire a certified electrician. So before you go out and find an electrical contractor, you first have to determine the kind of work that needs to be done.
What kind of work needs to be done?
Installing transformers for lights, fixing broken fittings, changing plugs on electrical appliances that came from overseas, and other seemingly simple jobs need the expertise of a trained professional. These jobs can cause damage and can even pose a threat to your life if not done correctly, so it is best to have qualified electricians do it for you.
Is the electrician qualified/certified?
The Wiring Rules (Australian Standard AS/NZS 3000:2007) is a set of standards set for electricians to comply to. When electricians have tested to be fully compliant to this set of standards, they are given certificates to prove it. These certificates are what you want to see from electricians you are considering to hire.
The relevant state regulator also issues electrical contractor's licenses. You would want a registered electrical contractor so you need to ask to see licenses when looking for the right one for you.
How reliable is the electrician?
You can ask around and talk to previous employers of the electricians you are considering. Ask them questions involving the quality of work and how easy the electrician is to work with. Do your research to determine if an electrician is trustworthy and reliable.
If you're having other things done in your home and you're working with a builder, ask them if they know a reliable electrician. You may even get a better deal out of it if you try to negotiate a bundle price for the builder and the electrician.
How much does the electrician charge?
It's important to get several quotes from different electrical contractors. You will get to see who's asking for a reasonable price or who's not. At this stage of the hiring process, you should already have a list of candidates.
Where is the electrician based?
It may not seem important now where the electrician is based, but you would want to consider it because you may need to have a follow-up job to be done. You would also want to have your electrician nearby when you want something done immediately. Convenience is part of what you're looking for in hiring an electrician.
Just remember that electrical issues, when dealt with by untrained people, including yourself, can cause injury or your house to burn down. Don't do it yourself even if it seems simple. Always look for the best professionals you can find.