@Greenfrost
It's easier than you think. First, you start off in Australia. Concentrate as much of your forces as you can there and quickly consolidate your territories early on. That +2 army bonus isn't much, but the advantage of a very secure continent that can only be attacked from one direction is no joke. Your next target is, naturally, Siam. Depending on what is going on elsewhere in the world, it's best if you keep a considerable garrison there and only move on once you're ready. From Siam, your goals are to take and hold onto China and India, which may require some diplomatic shenanigans with the rest of the world.
Once your position is secure, you may want to split your forces in two. You want an army in China to rampage across northern Asia in a beeline towards Kamchatka and then onward to Alaska, and another in India to secure two very important territories: the Middle East and Ukraine. Once that phase of the campaign is over, you have Asia's massive +7 army bonus, and you have also denied North America and Europe their +5 bonuses.
By this time, you will be the major threat and everyone else will try to gang up on you, but your position should be secure enough that you can advance at your leisure. If you have enough forces to hold Alaska, Europe will be a good next target. You will want to turn in a few cards this time to gain reinforcements, mostly for the army stationed in Ukraine. You will want to split that army in two, one to conquer Scandinavia and move on to Britain, Iceland and then Greenland, and the other to secure mainland Europe. You'd also want your army in the Middle East to take Egypt to deny the others Africa's +3 bonus.
From there, the campaign will be a simple southward invasion of Africa and a two-front invasion of North America from Alaska and Greenland. Do both at the same time; don't give the others any chance to somehow turn the situation around. Be careful if the others still have cards to turn in if you haven't baited them into doing that earlier, during your invasions of Asia and Europe. Some clever shuffling of alliances works wonders for this if you feel you don't have enough brute force. Once you've secured both Africa and North America and the others have still not found the good sense to surrender, then the fall of South America is little more than a walk in the park.
Congratulations, you have dominated the world.