When moving to the US there aren't many things more important than your money and the US banking system can be quite hard to get used to. American banks tend to be locally operated, so per state or region. Because of this local nature, those not familiar with the process can become quite frustrated quite quickly. Local banks are probably best avoided unless you plan on staying in that area, as cashing cheques from local banks whilst out of state can be tricky and other banks will charge you to use their ATMs. Instead, head for one of the bigger banks of which the main players are:
Some banks, particularly local ones will require that you apply to open an account in person and with proof of a US address but it is possible to open an account with a UK address, and don't forget that some UK banks will also permit you to open a US account such as the HSBC's Overseas Account services.
It pays to do your research however, and choose a bank that has branches in your local US region in case you need to visit in person.
To open an account you will need proof of ID and an address so take your passport, social security number (if you have one) and proof of residency.
The banking terms we use here in the UK will mean something quite different in the US so it's worth taking some time out just to try and make sense of the banking system and the different accounts available.
Thrift or Savings and Loan banks are the ones where you can both deposit and withdraw. A checking account is equivalent to a UK current account and a deposit account is essentially a savings account. You can manage your accounts in person, by telephone or through internet banking. You will also be issued with a debit card and can apply for a credit card through them.
Banks that provide mortgages and loans are referred to as Savings Banks.
Cheque books can be ordered for a fee, usually around $25 but you can get them printed in personalised designs if you so wish.
Overdraft fees can be expensive and be warned that unless you sign in to overdraft protection, you could find yourself in an embarrassing position at the shop till as your payment is refused. Typical fees could be $35 per overdraft purchase or for a set fee you could have protection meaning that overdraft amounts will be honoured and charges are considerably cheaper.
Debit cards are referred to as check cards in America however they are not used to guarantee cheque payments, only a photo-ID will do that and because of the high incidence of cheque fraud in America you may find that some places refuse to take cheque payments altogether.
Your debit card can be used in your bank's ATM but you will be charged for using another bank's cash machine.
Have a look at what British Expats are saying on the subject of US banks to hear more detailed accounts from migrants who are going through the system.