Okay have you read this: http://codex.wordpress.org/New_To_WordPress_-_Where_to_Start
A bit of reading up in the beginning will really pay off and help make the process of setting up WordPress on your hosting a lot easier.
Basically WordPress is a PHP-based web application that runs on a server. It requires a database (MySQL). So you need to make sure your hosting allows this - the ability to run PHP and MySQL with your particular hosting service plan.
The next step is to set up a database for your future WordPress installation. Make sure to note the database name when you create it, and also the database username (likely this will supplied by your host) and that database user's password (also likely supplied by your host). You will need this when "installing" WordPress.
Next download the latest version of WordPress and unzip it on your desktop. Then copy these files up to your server into the root website folder (or into a directory where you'd like WordPress to be installed).
Next, using a text editor (not Microsoft Word!) or code editor, open up the wp-config-sample.php file on your local machine.
You will notice that this PHP code has helpful documentation explaining what information needs to go where in this document. Also read through http://codex.wordpress.org/Editing_wp-config.php to see all the wp-config.php options you can set and what they do.
Okay so you've now inserted the database information and set the Security Keys (this stuff is used to help "hash" your passwords and session data helping to secure and protect your information - do make sure to use it!). Save the wp-config-sample as wp-config.php and upload it to where you installed your WordPress files on the server.
Now point your browser to your domain and to the particular directory of your WordPress install. You may need to potentially change your server settings via your hosts control panel to make "index.php" the "home page" of your domain.
You should now see the WordPress installation screen which lets you finish up the initial setup of WordPress. If you don't see anything or see an error message, try contacting your host for support as most issues are less to do with WordPress and more about how a server is configured (or mis-configured as the case may be).
So yeah, read-up and welcome to WordPress!
After that, we can cover how to install WordPress themes (which do require WordPress to use).