As someone who's installed Word Press about 5 different times on 5 different blogs, you can do it!
Here's my "Word Press for Dummys" guide.
1. Make sure your host sets you up a mySQL database in advance. Tell them you need to know the database name, the username and the password for the database.
2. Open the wp-config-sample.php file in a text editor and at the very top they are gonna ask you for the username, password and database name of your mysql database. Just plug those in and then "save as" wp-config.php. (remove the word 'sample')
3. Upload everything from wordpress that you downloaded.
4. Open this in your browser:
http://www.yourdomain/wp-admin/install.php
(obviously replace 'yourdomain' with your actual domain name)
5. It will walk you through the steps to install it. It just asks for an email address and blog name and some other easy stuff. It will issue you a random password to login at first that can be changed later. Remember this password until you login for the first time.
That's it! It should only take you 5 minutes!