That’s easy.
Just don’t use the Gmail app, but instead go to mail.google.com in your browser. There, you can sign in and out just like on a “real” computer.
Keep in mind that while what you are doing is perfectly reasonable, it’s not really how Google (or Apple, for that matter) expects most people to use their tablets. Therefore, there are a few simple steps you should take that aren’t really in the manuals.
The most important, I think, would be to create a new Google account which isn’t associated with any of of your family members, but with the tablet itself, instead. Let’s say your family name is Smith, create a new Gmail account named something like
thesmithfamilystablet@gmail.com. Use that account only as
the Google account on the tablet. (Android devices don’t really work too well with no associated Google account at all, but since several people share your tablet, you wouldn’t want to use any individual person’s account.)
That way, you get all the important Google notifications important for the apps and your tablet to keep humming along well. You can also use this account to manage your apps in Google Play (formerly known as Market). There is no need to link a credit card to that account, if you don’t absolutely need certain paid apps. (I’ve never bought anything through Google Play/Market and I have used hundreds of fine apps.)
That’s it, really. Use this shared family account for everything that all family member can see and things should work just fine.