Sure, I can give you some tips.
I am an Australian Pilot working in the North East of the USA, been here for about 2 years now, on a H1B tempory permit.
The easiest way to work here is to marry a US citizen. It won't take long to get your right to work here after that.
You can also get a US company to sponsor you for a H1B.
That may mean coming here or ringing them up, getting a foot in the door, then getting a lawyer to do the red tape side of things. That process can take anywhere from two to 4 months. (about a $1000 US) I strongly recommend a lawyer, so you don't have delays.
The H1B is valid for 3 years, and renewable for a further 3. If you get in with the right company, they'll probably 'sponsor' you for a green card once they know you alittle more.
And flying jobs are starting to gain momentum here, so this is an option.
I phoned different companies, and ended up getting a job that way.
You can also enter an annual "green card lottery". You enter into the draw in November/December and if your lucky enough, lightning may strike and you could get one that way.
For more info, goto
http://travel.state.gov/2004.html this is a free service.
later