Magento Installation Guide
This is a step-by-step tutorial on quick installing Magento on one the Hostmonster
hosting accounts. If you have any questions, please check Magento Support Forum. New questions and discussion are welcome.
Still there is an alternative manual installing way.
Step 1: Open Simple Scripts
To do so login to the cPanel for your domain and click on the Simple Scripts icon under the Software / Services section:

Click on the „Magento":

Step 2: Setup Wizard
After agree to the license and set your locale settings, click on the "Install Now" button to start installation.

You're Done!
That's all the configuration you need to do. Follow the rest of the instructions until you are finished.