Sticky Tape! Normal Sticky Tape works for me and the set does not budge one bit!
It's easy to do.

Plain old tape works just fine for me. I tried blu tac and it didnt work out .

A few dot's of my special, home-made extra-sticky sticky tack under the corners of the baseplate does the trick.

I use blu tak and occasionally tape as well, but whilst im animating i just take care in making sure i dont move the set accidentally.

I used to use gorilla tape, Until I broke my old baseplate. Then I just started using blue tac and masking tape.

I use plasticine and Blue tack and it works fine for me.

my structure/table i use to animate on is held together with tape

Dwalsh, Please don't triple post, it spams up the thread. Next time, please just select the 'Edit' button next to every one of your posts, and add onto it: especially when all 3 of those posts were 3 minutes from each other.

First, I smear 3 gallons of super-glue onto my table and plop my set onto that. Then I nail the baseplate to the table with 4 inch long nails. Finally I set up the camera, which gets the exact same treatment. After I animate I throw the lot into the trash and go out to get new equipment. I really need to get a new method.