The official ESTA fee is currently $40.27 USD and applications should only ever be made through the official US government website. Approval normally arrives within minutes or hours, although the US authorities advise allowing up to 72 hours.
An approved ESTA is generally valid for two years, or until your passport expires if sooner. It allows multiple visits to the United States, with stays of up to 90 days at a time.
When applying, make absolutely sure every detail matches your passport exactly. Be completely honest throughout the application process. Errors or inaccurate information can lead to refusal or problems at the border.
If you are refused an ESTA, you will usually need to apply for a full US visa through the American Embassy in London. Visa appointment availability can be limited, so do not leave this until the last minute.