Is this for a new business or existing business?
New business
Consider using a thesaurus online or offline and searching for words relating to what your company does. Go to a domain reseller or registrar to further explore your options based on the words returned from the thesaurus searches.
Make sure you don't infringe on existing trademarks, if not register your new domain name with the Patent and Trademark office so others cannot infringe on your rights.
Established company
Check if your company name is available using a domain registrar or reseller. If its not available consider using AfterNic.com to negotiate on your behalf with the existing owner. However, you may find the current domain name owner doesn't want to sell.
Both New and Established
Consider buying variations of the root domain (i.e. com, net, co.uk, etc). Also, look at registering domain names that relate to your product or service. For example, carsales.com, carparts.com, etc. Also consider purchasing common misspellings of your domain/s.
Registration and Web Hosting
A registrar is a service that adds your domain name to the worldwide domain name service (DNS). An annual fee is normally applicable to retain registration of the domain, but some registrars will allow you to register the domain name for multiple years in advance.
Web hosting companies usually provide a number of services. Most commonly the services provided are space for your website files, internet connectivity and email. Farbyte offers UK hosting web services that provide this and much more.
There are many aspects to Search Engine Optimisation (SEO). We will cover some of the basics here.
Keep your site content fresh and dynamic. This keeps existing users coming back and, in addition, new site content is crawled by search engine bots, causing sites to show up earlier in search results.
Obtain quality links to your site from other related sites, using relevant keywords and phrases as the anchor text and, if possible within a body of text as opposed to a solitary link on its own.
Make sure your site is easy for the search engine bots to navigate. In order to do this, try to avoid deeply embedded HTML structures.
If you are using graphics with lots of text in them make sure you complete the 'alt' attribute with the same text. The bots can't read images!