How can I keep cPanel up-to-date?

Login via SSH first. If you don't know how to do this, please read this article: https://support.tilaa.com/entries/20925478

When logged in as root you should run the following commands:

cd /usr/local/cpanel/scripts
./upcp # Updates cPanel software
./easyapache --build # Updates Apache and PHP

Please take a look at http://docs.cpanel.net/twiki/bin/view/AllDocumentation/WHMDocs/CpanelUpdates for more details