In order to use Gmail/Google Apps for your mail, you'll need to follow these steps.

Do note that at any point if these steps aren't adhered to properly, your mail will cease functioning entirely.

Step by step instructions on changing your MX entries to google: 

1. Login to cPanel for the domain you wish to use Google Apps/Gmail for
2. Select the "MX Entry" section
3. In the dropdown, select the domain you wish to point towards Google Apps/Gmail
4. Begin adding the Google records in the "Add New Record" section (Refer at the bottom below for the values)
5. Once you've added the five records, delete the original record that has a value of '0'
6. Afterwards return to the MX entry page and ensure "Remote Mail Exchanger" (or Automatically Detect Configuration if you intend on changing it in the future) is set within the "Email Routing" section
7. You're all done! Your mail should begin delivering to Gmail/Google

The current known MX records are as follows, though you may wish to check Google's page for updated values.

Value / Destination: 

1 ASPMX.L.GOOGLE.COM
5 ALT1.ASPMX.L.GOOGLE.COM
5 ALT2.ASPMX.L.GOOGLE.COM
10 ASPMX2.GOOGLEMAIL.COM
10 ASPMX3.GOOGLEMAIL.COM

For Windows XP, Vista and Windows 7:

1. Open the Start menu.
2. Go to Run. (If you do not see the Run command search for "run" in the Search bar)
3. In the Run text box type: ipconfig /flushdns
4. Press Enter and your cache will be flushed. 

For MacOS:

1. Go to Applications.
2. Go to Utilities.
3. Open the Terminal application.
4. Type: dscacheutil -flushcache
5. Press Enter and your cache will be flushed.

For linux:

1. Google a solution :)