Everyone here lists their nationality on their CV from what I've seen. There are so many different people here for different reasons....you need to let people know where you're from and why you're here and able to work.
As far as discrimination goes, I've found being an American *helps* get work/interviews/etc. It's a stereotype, I know, but we do have a reputation for a very high work ethic!
I agree with Ashley....an agency is the way to go. They're very helpful and just know stuff!
The only real change to my cv and cover letter that I made when looking for work here was including a letter of recommendation from my former employer, and a sample of my previous work. This way, they didn't have to phone the US up for refernces, and the work I did there was evidenced and very clear.
Best of luck!!