Do you need a visa?
Holding a British passport gives travellers a huge amount of freedom to travel around the globe, in fact you can enter around 170 countries without a visa, however for visits to some countries (particularly in Africa and some of Asia) you will need to get a visa issued before you leave.
Some visas involve visiting an embassy and others can be processed on-line. Most visas involve having a range of very specific documents to hand so check the details carefully before you begin the application process. Most visas also involve paying a fee so find out what this is before you book to make sure it doesn't tip your holiday finances out of balance.
My favourite place to check out visa information is on the Key Travel visa database where you can search by country and find out everything you need to know. For complicated visas or if you live a long distance from the embassy it's definitely worth considering using a visa agency to help you get your papers in order and do the leg work for you.
For travel to the USA you will need a ESTA (Electronic System for Travel Authorisation) which takes at least 72 hours to be approved and costs $14. For more details and to apply go here.