How can a British citizen gain American Citizenship?
Well, there’s far more information on the subject than I could tell you in a few minutes. What you want to do is go to www.uscis.gov, the website of the United States Citizenship and Immigration Services (USCIS). It’ll explain the different ways you can obtain a green card, what you need to do, and more. You will also need a temporary visa if you want to live and work there for a year, which it also has information on. If you don’t have family or a job in the U.S., or some special qualifications (e.g. a doctorate) pretty much the only way of obtaining a green card is via the “Diversity Lottery”, which is basically a yearly lottery on who gets a green card.
You cannot just apply for a greencard on no basis. You need to have either a close family member who is an US citizen sponsor you (e.g. spouse, parents). Or you need an employer who sponsors you. The latter is rare and practically non-existent if you don’t have any advanced qualifications. You can either try to find an au-pair program or similar, though they often cost money or you can see if you can study at a british university which has an exchange program with the US. There can be also other programs like Earthwatch where you can spend some time in a different country, but they usually cost some money. The only other option is taking a vacation and not working. You are not going to get a work visa for a job which doesn’t require any qualifications. Before you fill out form I-485 you need to have an approved I-130 or I-140. Paying about $1000 non-refundable submission fee for form I-485 would be a waste of money. You might as well throw that money out of the window.