Hey Joshua,
There is a lot on the web on this topic, but one of the main steps is to get a secured credit card - These will be issued to virtually anyone but the terms vary a great deal depending on your circumstances and it is a great way to get your credit performance tracked immediately.
A bank account can normally be opened based on your employment contract - but it may not be a debit checking account initially.
Check with the same bank if they run a secured credit card scheme as they are likely to look favorably on money passing through your account.
Typically, a UK expat with no credit history may be given a secure card with just an 800 dollar limit and may have to lodge a 300 dollar deposit for example as security with the issuing bank. You may find a much smaller deposits or even 100% of the full credit limit asked for as a deposit depending on the lender and your salary level.
Use the card for everything you normally spend - Groceries, gas, entertainment etc and clear the balance on time, each month and you will find your credit becomes established surprisingly quickly and your limit increases. They will reassess your credit on request after 12 months.
After a payment or two, you can use your visa card on the application for a store card account for a major (national) department store - buy a suit, clear the balance and leave the account open.
For vehicles - Big deposit is the key. Head for a main dealer, who may propose a lease option anyway (with your secure Visa) but apply for a large deposit purchase.
If you don't have the cash to hand, finance a large percentage deposit (75% of purchase price) as a personal loan before you leave your UK residency (you don't become officially non resident from the uk until after one complete tax year abroad, so it's all above board) and ask the US dealer to finance the only the remaining 25%. There is often very different lending criteria for small percentage finance as the risk to the lender is very small and this gets you onto main scheme finance.
Good luck
