Once you sign up your domain for Google Apps, you will have to change the MX records for your domain in order to use it in Gmail.
If you are using cPanel, this can be easily done by using the MX Entry option. There find the domain you will be pointing to Google Apps Mail and delete all of its MX records.
Then add the following MX records with the corresponding priority for your domain:
Priority: 1 to: ASPMX.L.GOOGLE.COM
Priority: 2 to: ALT1.ASPMX.L.GOOGLE.COM
Priority: 3 to: ALT2.ASPMX.L.GOOGLE.COM
Priority: 4 to: ASPMX2.GOOGLEMAIL.COM
Priority: 5 to: ASPMX3.GOOGLEMAIL.COM
Priority: 6 to: ASPMX4.GOOGLEMAIL.COM
Priority: 7 to: ASPMX5.GOOGLEMAIL.COM
The above instructions are in full compliance with the official Google Apps instructions and have been adapted to work with cPanel. They will require 24 hours to propagate and take effect. After that your mail will be handled exclusively by Google Apps Mail.
If your host does not use cPanel, you will have to find another way to change the MX records to Gmail. Still, the changes will be very similar to the above and the DNS records will be the same.
Gmail has proven to provide the best mail experience even to the most demanding users. That's why all web hosts should provide easy means to change the MX records to Gmail.