Picasa Web's help center explains that you need to create a new Google Analytics account (not a new Google account) to monitor Picasa Web Albums photo traffic. After creating the new account, find the account ID that looks like UA-xxxxxxx-y and enter it in the Google Analytics tracking code box from Picasa Web Albums. "Once the setup is complete, just sign in to Google Analytics and click View reports to see visitor stats for your photos. It can take up to 24 hours for Analytics to detect your tracking code."
A similar option is available for Google Docs, but only for published documents. While this feature is useful, it's not very easy to use and it's not properly integrated with Google Docs and Picasa Web. Showing simple stats, like the number of views, the top search queries and referring websites, in a special section of Google Docs and Picasa Web would be a much better idea.