Registration fees are generally minimal. For example, many registration agents for .co.uk names charge around £10, or include the domain name as a free part of a service package such as website hosting. You will also have to renew your registration, typically every one or two years. Renewal fees are at a similar level.
If, however, you are buying a domain name from someone else, the purchase price is a matter for negotiation. In the past, some particularly catchy domain names have been sold for tens or even hundreds of thousands of pounds.