Wordpress uses PHP which is only available on Supporter accounts.
Download and unpack
Download and unpack the latest version of WordPress (version 3 when writing this):
wget http://wordpress.org/latest.tar.gz tar xvzf latest.tar.gz
Rename (and move):
mv wordpress public_html/blog rm latest.tar.gz
Set up MySQL
Edit the WordPress config file:
cd public_html/blog mv wp-config-sample.php wp-config.php nano -w wp-config.php
Enter login details for the database, DB_HOST should be localhost.
Run installer
Next, surf to: http://<username>.blinkenshell.org/blog/wp-admin/install.php
Enter blogs name and email, press next.
Copy the password and save it in a textfile or something.
Logging in
Go back to your blog: http://<username>.blinkenshell.org/blog/
Login with "admin" and the password you saved in a textfile before.