First up you'll need a boat, a tinny will do as it is quite cheap.
To get to the USA you'll want to jump into the water on the east coast of oz and catch the East Australia current that'll take you into the south pacific. If you head too far south catch the west wind drift, stop when you hit south america then catch the Peru / humboldt current. This will take you to the USA for nothing more than the cost of the tinny. I think it will take quite some time but this can be decreased by investing in a paddle.