So once you have your domain and your webhost setup, you're ready to install Drupal.
(if you're not a fan of reading, you can skip down to the video)

Setup Your Database

The first step is to setup a database for Drupal to use.  If you're using cPanel, you'll login to your account then find the "Databases" section.  You'll want to click on the MySQL Database icon.  Your version of cPanel may look different.





You'll then enter your database name, and click "Create Database".  After that, click "Go Back", and scroll down to "Add a User to Dataase".  If you haven't created a user yet, you can do that with the "Add a User" section just to the left.



You'll want to give the user "All Priveleges".

Download, Upload and Unzip Drupal

Next you'll want to head over to http://drupal.org/ and download the latest version of Drupal (6.2 as of this writing).  After you download it, you'll need to upload it to your webhost. 

Upload this to your hosting space using an FTP Program or CPanel's built in File Manager.

After it's uploaded, using the File Manager, you can extract the contents of the file by clicking on the file's name and then select extract in the menu in the upper right (again, your version of cPanel file manager may look different).


 

This extracts the whole package into a folder named drupal-x.x. You will then need to move the files out of this directory and into your document root directory (ie: public_html or www).

You can also extract all the files on your computer and upload them via FTP, however this may take significantly longer.

Note:  Make sure that the file .htaccess is in your document root.  without .htaccess, your Drupal site will not work properly.  Depending on your File Manager setup, you may have to move this file from the drupal-x.x folder to your document root using FTP.

Install Drupal

Next, open up a web-browser and type in your domain name.  This should bring up the Drupal installer.




We'll assume an English installation in this case, so click "Install Drupal in English".
This brings our database setup screen.



Enter your database information that you decided on in the first step.  Hopefully your host is setup to use "localhost" as it's database hostname, as "localhost" is what Drupal will use by default.  If not, you'll need to click "Advanced options" to enter the database hostname.

Then click "Save and continue".  Hopefully you don't see any errors, and the installation commences.  If you get an error, it's often due to incorrect database credentials, or an incorrect database host (ie: your setup requires something other than "localhost").

Assuming all went well, you should be presented with a screen like this:



If so, all is well with your installation.  Fill out some basic information about your site and click "Save and continue".

That's it!  Your Drupal site is now ready for exploration.

Here's a short video outlining the Drupal installation method above.

Note: this is only one way to install Drupal.  There are numerous ways you can setup a database, unzip your Drupal package, etc.
Here are some other tutorials that you may find helpful.

• A videocast from Lullabot about installing Drupal 6.
• Installing Drupal using cPanel