When I went to see Liverpool at the start of the year I used this site:
http://www.thesportsboxoffice.com/Premier+League/
Basically order the ticket online then they ask for a delivery address. I don't know if it's changed since I did it but they asked me for a UK address to deliver it to because they only issued the tickets a week before the game, so obviously you don't want it sent to Australia at that time. That was just my experience though - I just looked at the site and you can definitely put an Aussie address there, but be sure to check with that they can send it to Australia well before the game, else just give them a UK address.
The good news with this site is you get the ticket guaranteed. The bad news is how much it costs. But in saying that, it is the Premier League, you'll be paying top dollar pretty much any way you want to get in. I saw Liverpool vs Everton at Anfield and it cost 300 pounds

Although my attitude was that I was only there once, I wanted to see it and had the money to spend, I wanted minimum fuss and got it.
You can also call the club, tell them you're a fan from overseas and see what they can do for you, but your best bet with this is to do it for a low key kind of game. If you're wanting to go to a derby or another big type game I wouldn't even bother.
Touts and scalpers are definitely an option, although I don't know much about it except that at the game's I went to they're outside the ground going up to people and asking in hushed tones "Want a ticket?"
Again, don't know anything about it or whether there's some stories out there about people being sold dud tickets, but if you're prepared to do it, be prepared to pay top dollar for the ticket and do it discreetly.