As others have said, a checklist is critical. If you don't know what they had access to, there's no easy way to revoke it. Don't forget that people might also have access to external accounts on behalf of the company (like support contracts for Oracle or something like that, in addition to Google apps and such) and you'll want to be able to secure those as well.
What happens to their emails?
Old emails? Well, it depends on whether you think there is anything useful in there. While it is prudent to archive them, my experience has been that everything will be overcome by events and decisions that no one is likely to ever search those emails for information. Basically, whatever the archiving rules are for everyone should be followed for the exiting employee.
New emails sent to their account? If they were getting emails from outside related to the business it's smart to redirect any mail sent to their email address to someone else in the office. A small company for which I do some work had the office manager leave a few years ago and they still get some emails for her email address that the current office manager needs. A lot of website accounts get linked to email addresses and it would be shame if you couldn't do a password reset on one of those without having the account any more.
How long should you wait before revoking their access?
It depends on how they left. In some cases, I've had access and consulted back to former employers for years. If it's a hostile termination, revoking access before informing the employee may be prudent. In most cases, the person keeps working until their last day, so you follow the same security rules you have for everyone - they only gets rights to what they need to in order to do their job. Revoking access immediately might both piss off someone who thought they were leaving on friendly terms and inhibit them from transitioning their tasks to other team members or their replacement.
Should you do a general clean up of the system they used to work on?
Of course. There's a good chance that they might accidentally leave behind personal files or leave cookies with IDs and passwords behind on the computer. You don't want to expose the departing employee to identity theft or your company to any liability for making that possible.