Once your account and email is setup with Google, to change your MX record to use Google Mail services log in to cPanel and go to MX Entry.
For the domain you will be pointing to Google Mail you should enter the following MX records, removing any other MX records that currently exist:
Priority: 1 to: ASPMX.L.GOOGLE.COM
Priority: 5 to: ALT1.ASPMX.L.GOOGLE.COM
Priority: 5 to: ALT2.ASPMX.L.GOOGLE.COM
Priority: 10 to: ASPMX2.GOOGLEMAIL.COM
Priority: 10 to: ASPMX3.GOOGLEMAIL.COM
The above instructions are in full compliance with the official Google instructions and have been adapted to work with cPanel.
IMPORTANT: The above changes will take up to 24 hours to propagate and take effect. After that your mail will be handled exclusively by Google Mail.
You can sign up with Google Apps email here: https://www.google.com/apps/intl/en/group/index.html