These are the most common questions I get asked on this site and on my Facebook page as well.
I hate to appear vague but I don't have any easy answer. I can tell you what worked for me (when I was a principal) and works for me (as a relief teacher).
When I was principal I hated making permanent staff appointments from a list of faceless names provided by the department.
90% of the staff I appointed came from relief teachers who had undertaken some relief teaching gigs at my school.
These relief teachers had built a relationship with school staff and some of the kids. They had usually exhibited loyalty to my school and, in turn, I offered my loyalty to them.
So I actively pursued these teachers during the staffing period to fill permanent or contract vacancies.
You have to remember that there are transfer processes that the system has in place. However, where possible I would fight to have some one who had been relief teaching at my school before going taking a name from the list of the "great unwashed ;>)"
Don't cast you net too wide. Select a few ( 3 or 4) schools that are a good fit for you. That is, schools where you feel comfortable. Let them (principal, admin staff) that you will make yourself available to them first. Do the math! In a school of 30 - 40 class teachers - 2 or more teachers are going to be away EVERY day. There will be several vacancies for relief teachers available every day. If they know they know you are one of the relief teachers on call, they will call you first.
When I was principal (850 kids - 33 class teachers +12 specialists) we had four regular relief teachers who filled 90% of our relief teaching vacancies. We always had at least 2 vacancies, most days 3 or 4, sometimes as many as 8.
If you are relief teaching in say 20 schools and getting the occasional day in each (say once a month) you could be working full time. But would anyone in the school remember you?
Let's say you select 4 schools and do say 5 days a month of relief teaching in each, you have a much better chance of being memorable. It might take a little while to become a regular for those schools, but it will work.
Obviously, if you are surrounded by smaller schools, relief teaching vacancies may not be so regular so you might need to select more.
As you get yourself established in your chosen, don't knock back anything.
I had a young teacher who did a small relief teaching contract for me as a music teacher, another small contract as a LOTE teacher, she filled in on a younger class and again on an older class. She was tenacious. I know some of the work was difficult for her but that dedication was noticed by the other teaching staff and my admin team. So when a full time vacancy came up, she was the first person who came to mind. Consequently she end up on my permanent staff - and still is.
Be aware of the limitation of some relief teaching employment agencies. These are agencies who fill holes. You are a number and they fill vacancies with a number.
Let your schools know that you are on ClassCover and they can find all your contact details on that site. If they are not a member, they should be.
Prepare and refine a couple of fabulous lessons. When I started relief teaching I refined a lesson based on Banjo Patterson's Geebung Polo Club. I loved it, the kids loved and it became a bit of chatter around the school. Teachers knew that when I visited their class, I would do this lesson. And so did the kids. In fact, I think some were looking forward to it.
I eventually turned it into a teaching unit for some longer relief teaching stints.
The point is that a couple of fabulous lessons get noticed.
When you find a school that is a good fit and you want to stay longer at, buy yourself a couple of coffee cups with your name on it and leave one of them in the staff room. That way when some one sees it and asks, "Who owns this cup?" your name will be mentioned in the staffroom - which one day might be yours!