According to Gmail Guide, the following steps need to be provided to Google in order to obtain access to the Gmail account:
1. Your full name and contact information, including a verifiable email address.
2. The Gmail address of the individual who passed away.
3a. The full header from an email message that you have received at your verifiable email address, from the Gmail account in question. (To obtain the header from a message in Gmail, open the message, click 'More options,' then click 'Show original.' Copy everything from 'Delivered- To:' through the 'References:' line. To obtain headers from other webmail or email providers, please refer to http://www.spamcop.com/help_with_headers/)
3b. The entire contents of the message.
4. A copy of the death certificate of the deceased.
5. A copy of the document that gives you Power of Attorney over the Gmail account.
6. If you are the parent of the individual, please send us a copy of the Birth Certificate if the Gmail account owner was under the age of 18. In this case, Power of Attorney is not required.
Gmail Guide requests that you send this information via Fax or Postal Mail:
Attention: Gmail User Support
1600 Amphitheatre Parkway
Mountain View, CA 94043
It takes approximately 30 days for the information to be processed, but if the access is needed sooner, "it is Google's policy to only provide information pursuant to a valid third party court order or other appropriate legal process."
Discussion continues at Google Groups.