Step 1: Register a domain. Using GoDaddy or your other favourite domain registrar get your own domain name registered. Time required 5 minutes.
Step 2: Get hosting. You can spend hours and days researching web hosts. To do this as fast as possible look at a decent WordPress host. I recomend Hostgator, but there are several good WordPress hosts. If you already have a hosting account somewhere you can probably skip this step and simply use an addon domain on your current hosting account. Time required 25 minutes.
Step 3: Change nameservers. This step only takes a few minutes. You need to login to your registrar and set your new domain name nameservers to point to your web hosting account. Time required 5 minutes.
Step 4: Login to your web hosting control panel and use their script installer to install WordPress. Most cPanel hosts have Fantastico to quickly install WordPress. Time required 10 minutes.
Step 5: Login to your new WordPress install and start writing! You have 15 mins left to spare to write your first post.
Now of course this only gets you the bare bones of a website. There is still a great deal more work to do like finding a new theme for your website and customizing it. Adding some plugins to help with different website tasks. Creating a Twitter account to help promote your new website. Creating a Facebook page. Taking the time to update your website regularly with new content. Well, you get the idea, but setting up the core of a website can be done in less than an hour.