1. Download WordPress. Be sure that you get the latest version. Once it's downloaded, unzip the folder onto your hard drive.
2. You will need to make a database and a corresponding user. This typically is done in the control panel given to you by your server company. First create a database with an easy to remember name. Then make a user for a MySQL database. Write down the username and password you inputted. Also be sure to give the user maximum privileges.
3. You will then need to customize the wp-config-sample.php file. This file is the folder you unzipped in Step 1. First, rename the file wp-config.php. Then enter the proper information for DB_NAME, DB_USER and DB_PASSWORD that you created in Step 2. When finished, re-save the file.
4. It is now time to upload the contents of the downloaded folder to your server. The easiest way to accomplish that is by using an FTP. You can decide to upload the WordPress onto root directory (www.YourDomain.com) or a subdirectory (www.YourDomain.com/sub).
5. The last step is to run the installation. You can find the script at /wp-admin/install.php in the directory you selected in Step 4. Simply visit the URL in your web browser and the install script will run. Follow a few easy on-screen directions and the installation of WordPress onto your domain will be complete!
If you run into any problems, check out the WordPress codex. If you are new to blogging and don't want the hassle of installing the software on a server, you can instead opt for letting WordPress host your blog. Doing so is free and you will join over four million other blogs. Find out more at WordPress.com.
You can also choose a WordPress auto install option, available through many web hosts. Check your web hosting control panel to see if WordPress is one of the one click install options.