The easiest way to install Typo3 on your account is from your cPanel-> Softaculous. This can be done by selecting Typo3 from the Portals/CMS section on the left and clicking on it. When the page for Typo3 is loaded, click on the "Install" tab.
Select the domain where you want your Typo3 to be installed and the installation directory.
Leave that field blank if you plan your Typo3 to be installed in your public_html, i.e the root of your webserver. You can also enter a name for directory. Please note that if the directory is not existing it will be created throughout the installation process. Fill in your Administrative details and click on Install Typo3.
TYPO3 can also be installed manually. For further assistance you can refer to the following tutorial:
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