Domain name and Hosting space

Domain name

Domain name is the name of your website, ie: www.whaever.com
The problem with very cheap domain registration is that the registrar company might charge you a lot of money to move your domain to another one if you're not happy with the service
Google prefers domain names that have been registered for more than one year
Ask for a UK-based IP or .uk domain or .com in a uk based company, as it identifies a site as being "British" and this is good for SEO

Hosting space is a physical space in a server computer to upload the files needed for your website.
Ask for: Operating System: Linux (more reliable and cheaper than Windows) | Server side programming: PHP (free and cheaper) | Data Base: MySQL (free and open source database)

Registrar company: to buy a Domain name
Webhosting company: to buy a Hosting space
Most of the Registrar companies offer as well Webhosting, so it is best to buy both products with the same company
Companies: godaddy.com (recommended) | 123-reg.co.uk | fasthosts.co.uk | uk2.net | 1and1.co.uk
Keep all the login and passwords for: the company where you bought the products | control pannel | FTP

Go to your Registrar company > Enter in your account > Select your Domain > Select NS (Name Servers) > Change them with the ones provided by your Webhosting company (look in the welcome email).
Your site will start working in 24 hours, may be sooner.