1. All directories should be CHMOD to 755 while all files should be CHMOD to 644.
2. If you are using version 1.1.0 (Beta) or 1.1.1 (Stable), be sure to rename the php.ini file to php5.ini.
This article is a quick step-by-step tutorial on installing Magento Commerce on Aspiration Hosting Aspire™ Shared Hosting account.
You can find the latest Magento installation packages at the Magento Download page.
There you can select the preferred archive format and version - light or full (full includes sample data - stores, categories, products, images, etc) you want to download.
Upload the extracted files to your web server via FTP to the “public_html” folder (important) which is under your domain folder (usually yourdomain.com).
Set up the permissions on files and directories via your FTP client or your cPanel File Manager interface. Ensure that all directories should be CHMOD to 755 while all files should be CHMOD to 644.
Go to MySQL Databases of your cPanel, create a database, a MySQL user, and password that Magento will use.
Use your web browser to surf to any Magento page (for example /magento or anything) and you will be forwarded to the installation wizard.