How I did it was manual, since Cpanel (fantastico) to my knowledge doesn't support 1.5 yet.
Assuming this is on a cpanel hosted server and this is also not a step by step instruction but a fair summary for install.
If you want to test, create a sub folder in your www or public_html directory.
By using the file manager through your control panel, upload the Joomla 1.5 latest zip file into the test folder. Or if you are using Sea of Glass template, upload the file called SiteShaper_Shape5_SeaofGlass15.zip.
Run the Database admin wizard from cpanel and create a database, user and password. Write those down as you will need it for later to put in the info when you go through the wizard.
Open a browser and type in your URL: www.yourdomain.com/testfolder_name
It will launch the installation wizard. Click through and follow the instructions. For the database server, usually you type in localhost and the rest is from what you created from the database wizard. Install the sample data.
Once you complete the install, delete the install directory.
To access the administrator panel, www.yourdomain.com/testfolder_name/administrator
Login and you're good to go.
Once you feel comfortable testing and using, you can move it to your root directory and it will be live.. you may have to rerun some file path configuration, but that's pretty easy to do.