To enable compression within your web hosting package, log into the cPanel interface.
Once here, look for the menu item "Optimize website".
To enable compression, change the setting from "Disabled" to "Compress all content" as shown in the screenshot below.
If you want to add MIME types or base the compression on completely custom rules, use the menu item "Compress the specified MIME types" and fill in the field according to your requirements.
To find out which MIME types are stored in the standard system, click on here.