You need to come up with a name that isn’t already taken by someone else. Domain name companies will help you to search whether a name’s available, and if so, to register it.
You probably want your domain name to be the same as your business name. If you haven’t yet finalised a name for your business, you might want to hold off doing this until you’ve checked that your proposed name is available as a domain name.
You need to register the extension – the letters that come after the dot in the domain name. The most common is ‘.com’ but to avoid getting confused with other businesses, you’ll probably want to register names with multiple extensions (e.g. ‘.co’, ‘.biz’, ‘.uk’ etc).
You’ll need to pay for each domain name, and also for annual renewals. Typically, a ‘.com’ costs about £10-15 a year. Others like ‘co.uk’ may be under a fiver a year, but one like ‘.london’ can set you back £25 or more per year.