Travelling via the US?
All passengers who fly to the US, even if they are only in transit (changing planes) must apply for an online ESTA (Electronic Travel Authorisation System) visa before travel. Previously, the visa was free of charge but a couple of days ago a charge for the visa was introduced. There are a lot of websites out there offering visa services and they will charge you the cost of the visa plus an admin charge, so typically they are not good value. The official website is https://esta.cbp.dhs.gov and this is the best port of call to avoid any unnecessary fees.
You also might find the following information useful:
Passports must be valid for 90 days from date of entry to or transit in the US. ALL passengers must have a machine-readable passport. If your British passport is machine-readable it will have at the foot of the personal information page (at the back of the passport) two lines of text as letters, numbers and chevrons (>>>). If there are no lines of text, the passport is not machine-readable and you need a visa. Avoid locking your suitcases if you are transiting via the states - their customs officials retain the right to break into them.
See my colleague Claire's guide to transitting Miami Airport. Not for the faint-hearted!