What kind of site do you want?
If it is a blog you're after go sign up to tumblr, free, and play with the look and feel of it (under the customize tab).
If you then want to look more professional you could buy a domain name (from someone cheap like 123-reg). Tumblr has a really easy, straight-forward way of having the domain point in the right direction.
I only suggest Tumblr for its simplicity - others may have better ideas about free platforms more fitting to what you're doing.
All the best,
Spare Ed
P.S. My friend set this all up in a matter of minutes for their charity cycle ride:
http://home2rome2010.co.uk