What version of InDesign are you using?
Eugene, thanks for your response and please forgive my stupidity for not including the version which is, CS6. I have used the forms and buttons function to build fillable forms and it works well. I attempted a couple of tries to make individual table cells fillable and could not find a way to make it work.
That's because you can't. You'll need to create the buttons / fields for each cell.
Perhaps the ears of Adobe will pick up on this and "figger" out a way to make that happen in future versions.
This is a user to user forum - Adobe employees rarely visit. And the wishform that Bob points to is great, but unless it's a feature that's requested by a lot of users, it most likely won't be integrated to newer versions - but who knows.
I think a good bet for now is to visit the Scripting Forum and perhaps someone can help you streamline the process by creating a script.
Hope that helps.