The easy way:
Create an account at blogger and begin (there are other free blogging services, if you prefer).
Your domain name will be [something].blogspot.com, so to be more cool you can purchase a domain name at yahoo for only $4.98/year. Simply forward it to your blogspot address.
The better way:
If you want to do more (e.g. have a database, dynamic pages, email accounts, etc...), you can get a web hosting plan. Examples of what you can do with this are the discussion board, ugly picks page, stock screener, portfolio, and the barchart charts page. You can do this through yahoo, but it is much more pricey and not worth it. I suggest getting it through me - I do a reseller program with my web hosting service company. I will give you $5 off of the already very low price that they mention on their website. So for only $55/year, you get more than enough to keep you busy - check out everything they have to offer. If you are interested, send me an email.
Once you have your own hosting plan, you can connect it to blogger and get started.

If you have questions, let me know.