We'll start with the VERY basics.  To use Drupal, you need a server to install it on.  This could be your own computer, or a hosted computer.  I'm assuming you're going with a hosted computer, so other people can access your website.  This means you'll need a webhost.  Most webhosting companies are sufficient, though certain configurations are definitely favorable for Drupal.  More on this later.

Pick a Domain

If you haven't already, you'll need to buy a domain.  You can buy this from register.com, networksolutions, dotster, godaddy, 1and1 ... anyone you want basically.  Sometimes it's nice to have it be the same as your hosting provider, but you may want to keep it with a different company.  Up to you.  Wherever you get it, you'll need to be sure to set it's nameservers to point to your webhost once you have that part setup.

Pick a Webhost

Drupal's base requirements are found on almost any webhost you can find.  However, to make life easier, you'll want to be sure your webhost provides the following:

• supports PHP and MySQL. 
• You'll need either FTP access, or access to a web-based file upload utility.
• Either SSH access, or a web-based utility that allows you to unzip files on the server.
• Ideally, they access MySQL locally, ie: "localhost", rather than on a remote server.
• If they run cPanel as your 'management tool', great.  Others will work as well, but cPanel is pretty common, and does its job well.

While you don't need to know any HTML, CSS, or PHP to build a basic website using Drupal, it's helpful to have a text editor in case you need to edit any stylesheets or template files.  I'd recommend either Notepad++, or PSPad.  They're small, free and make editing HTML or CSS files pretty easy.

You should also have an FTP client (CoreFTP is a decent free FTP client), though you could use your web-hosts upload utility or Internet Explorer's built in FTP ability if you'd prefer.  You'll need this to upload the Drupal package to your webhost, and to upload any future modules you'll install later.

Lastly, you'll need a couple hours free to install, configure, and familiarize yourself with Drupal. 

Check out my hosting review site,  DrupalHostingReview.com, for an  up-to-date listing of web-hosts I've had experience with.