Assuming that you're a UK citizen, you're not eligible for the 'green card lottery' scheme for potential immigrants.
Therefore you can
only emigrate to the USA if you've either got immediate family members there or you can meet the every strict criteria for employment. (Typically you need to show that you've got skills that can't easily be matched by a US citizen, e.g. if you're a movie star, or that you've got relevant professional qualifications to masters' degree level).
Otherwise, like the vast majority of Brits, you
can't emigrate to the USA..
However, the simple solution would be to marry your girlfriend. Then (assuming that you meet the other criteria, such as having no criminal record for crimes of 'moral turpitude') you might well qualify for 'family based' immigration:
http://www.usembassy.org.uk/cons_new/visa/iv/i ndex.html
Chris