As a UK citizen you are allowed to visit the US on the Visa Waiver Program (VWP) which enables you to stay in the US for up to 90 days without a visa. HOWEVER... the VWP specifically prohibits you from staying beyond that time and for seeking work, and you are also not able to change your status to permanent resident. If you want to move to the US with work, then you'll need a work visa - the most common being H1B but there are strict quotas for these and they're difficult to come by because there are so few. If you're employed in the UK by a company who has subsidiaries in the US, then you may qualify for an L1 which enables you to transfer with your current compay to the US. Once you're there you can change your status to permanent resident.

Your other option is the DV lottery.

Moving legally to the US is a time-consuming, lengthy and pricy experience. I know, I'm in the process of doing it myself