Unless you're brave or close enough to take to the roads, you start by booking a flight into Boston's Logan International Airport. Boston is served by American, Delta, Southwest, United and JetBlue.
From there, you can either rent a car and drive straight to the Cape (about 90 min) OR get the Plymouth & Brockton bus from the airport to Hyannis or Barnstable and request a ride from there (Uber and Lyft do exist on the Cape, just not in massive quantities). The Langsen family has taken a lot of those buses over the years and this is a good option if you're coordinating with a larger group with a car arriving at a different time.
Flights from London to Boston Logan Airport include Virgin Atlantic from Heathrow and Norweigan from Gatwick, though we'd recommend the former over the latter. You can rent a car to travel from Logan to Cape Cod, or alternatively ride the Plymouth & Brockton Street Railway Co which we'd call a bus.
Those travelling to the US from the UK will need a valid ESTA, which can be applied for online and costs $14 (about £11). These are pretty quick to process so we'd recommend you fill in the form about a month before your flight. It's all electronic so you won't need to print anything out.
You'll need to fill out a landing card (which will be handed out on your flight) so it's usually a pretty good idea to pack a pen in your carry on luggage. Also, people who carry a pen always look smart.
May 27 also happens to be Memorial Day in the US, which is a federal holiday. Americans do not get a great deal of public holidays so this is quite a big occasion.
Americans drive on the right.