It's a pretty easy process however it can seem like a hard task if it's your first time installing a wordpress blog script on your web hosting account manually.
When you download the Wordpress script which is free there should be some instructions included with the Wordpress script.
What you need is an FTP client such as Filezilla to upload the files from your computer to the web server and then you need to create a database and username for the database in the mysql manager of your hosting account control panel and assign it a password.
You'll need the username and password for the database to enter when you get to the installation page of the wordpress script.
After you've unzipped the wordpress folder and uploaded the wordpress files all you need to do is go to the domain of your wordpress website and an installation page should automatically show up where you enter a few details and within around 3 to 5 minutes you'll be able to use your wordpress blog.
Most web hosting companies also have the option of auto installing Wordpress through the control panel as well without needing to upload the files.