Using your identity to brand your web page - favicon:
The graphic must be 16 x 16 pixels and it is best to use a 4 bit image
If you look around you may notice that letters tend to work well, as well that graphics that are framed by a square, avoid detailed images.
Purchasing a Domian
There was once a time where there was only one company that managed domains -
Network Solutions, this is no longer true. Generally, you may purchase and register your domain with the company that you choose to host your site with. If you purchase your domain separately from the host service, you may save money by buying the domain from a company such as GoDaddy.com.
Searching for a Host
Open Source Utilities
If you don't have Dreamweaver there are plenty of freely available editors as well as free FTP clients:
A personal favorite is jEdit
FTP: Filezilla; Cyberduck; Fugu
As blogging has become a cultural phenomenon to the extent that individual bloggers are acknowledged by the mass media, there are plenty of blogging kits also freely available (if you purchase a host service, blog engines such as WordPress may already be ready for install as part of your service):
Word Press
Movable Type
Blogger
An Open Source Hub