Hi AM
There are lots of companies out there who can help you.
I buy my domain names and webspace from this lot:
http://www.1and1.co.uk
They are cheap and I've never had any issues with them.
The first year's registration for a .co.uk domain is 99p, then 2.99/y. Peanuts.
Basically you go to the website, check to see if the name you want is available, click [buy] and within a few hours you have the domain name.
Setting up the website is also straightforward. You can either buy a package with your domain name (for example, the 1&1 home package includes webspace and email accounts for £2/m with ten free domain names or something like that).
Alternatively you could buy your hosting space elsewhere. There are loads of providers at varying price points.
One of the sites I don't update very much,
http://www.andyeccles.com is hosted for 50p per month, and I created the site using Joomla.
If you just want a simple few pages with some photographs, you could create it yourself and upload the pages really simply.
In terms of gotchas, not much -just avoid signing up to any lengthy contracts - you may want to change providers if you're not happy.
Clear as mud, eh!?
Cheers
Andy