Wotcha Si. Hunting in the US is as easy for us as it is for residents mate. You'll need to get in touch with an outfitter. Unless you know somebody who owns private land & is willing to give you permission to hunt it, it's really not feasible for us foreigners to arrange an entire hunt alone. Different States have different laws regarding hunting on public property & that's a minefield in itself.
The best thing I can suggest is to get in touch with one of the outfitters in the Sponsor's Ads & sort everything through them. I hunted, this year, with Curtis (7th Age Bowhunting) & had a whale of a time! Don't expect to have a guide trailing you everywhere, telling you what to do. From my own experience I was given a detailed outline of where I could hunt, where the game was being seen & then left to my own devices! Be aware that you'll need to purchase a hunting licence and, again, this is different in every State. Some are available 'over the counter' in sporting goods stores, some are postal only application & some are a lottery-type draw that you need to enter months in advance.
I would strongly suggest that you figure out where abouts you want to go. If you're after hogs (boar) try Texas/South Carolina/Georgia & the southern States. For Deer (you'll need to wait until season opens, sometime in October) again Texas is good as, I'm told, are Illinois, Ohio & the Central Eastern States (Ohio, Michigan etc) Once you've sorted out where to go, try & find a reputable outfitter in that particular State (Asking here would be your best bet!) Your outfitter will be able to tell you about licence requirements/fees etc. Then it's just a case of booking a flight & getting there!
If you need any more help, the guys here are GREAT for giving up information. If you've any questions about getting your gear to the US or deling with folks in the US, drop me a PM & I'll help out werever I can.
Good luck & good hunting mate!