That's one of the biggest hurdles to beginners, who usually don't own their own houses or furniture and don't have a space where they can build an animation table they can drill holes in.
What I did in the beginning was clamp a nice wide plank of wood along the front edge of a table. I was able to drill holes in that to my heart's content without damaging the table in any way. And it works surprisingly to stage all the action along the front edge of your set and just have set dressing behind it - after all, that's the background! It's not too often you need a long shot with the characters way off in the distance.
Another trick is to build a little mini-table, just a board with some legs under it that you can clamp on top of an existing table.
Don't use metal unless you're going to use magnets under the table and have solid blocks of metal in the puppets' feet. Some people manage to make that work but to me it seems pretty problematic.
The best kind of wood to use is something like particleboard or MDF (medium density fiberboard, which is like a much more fine-grained particleboard). With plywood when you drill holes you tend to get big splinters and spikes of wood that rip out leaving big gouges in the wood around the holes. These can be filled in but it's extra work and can make a set floor look pretty bad. That said, I'm still using plywood for mine and it works, but I wish I had got ahold of some MDF before building my table. You can get it at many hardware stores - just ask a helpful hardware man.
Ok, here's some pics:
This is my original animation surface. You can see some of the holes in it, and the fact that it's been painted a few times. It's obviously been a while since I animated here - now it's a place to store junk.
This is a mini animation table whipped up by Sven Bonnichsen. Both pictures are links, mine to Flickr where you can see it bigger, Sven's to his blog post abut making the tabletop table.
Thanks for the help! I will take this on board (pardon the pun).
Sure, no problem.
Oh, and what I said about not using metal unless you're using magnets - that of course doesn't apply if you're using perforated steel sheet like Sven did for his table. Personally I don't worry about drilling holes all over, I just create paths where I know puppets will need to walk in the upcoming shot.
I made a set for the first time about a year ago, so I might be able to make some suggestions. I am using a table top set that is reasonably compact. I am working out of my flat and have limited spare space. I was aiming to make something reusable without much rebuilding or heavy use of tools as I am working in my living space.
Essentially everything is attached to a single 6mm MDF board that has three wooden struts/supports screwed to it. The board lies flat on the table and the struts point upwards. I then place new floors on top of the struts for each new scene or as required. I can easily take the floor out to drill out holes for tie-downs. I have only been securing the floor by pushing it against the walls, and sometimes using wood tacks.
I can add back and side walls using additional MDF boards by clipping them to the struts. I like this method as I can put in and take out walls without glue or screws. All I had to do was leave enough gap between the struts so there is room for a big plastic clamp. This also means I can flat pack it a bit.
Generally I have been dressing the set by clipping cardboard to the walls on the outside edges, and pushing the removable floor against the walls to pin the cardboard against the wall on the inside edges. I hope these two pictures help it all make sense. They are from different scenes at different levels of construction though.
I am going for a Dynamation style set-up, with a green painted board acting as a matte green screen (suggested by Peter Montgomery) and the animation table as a base.
I will upload some pictures of my current animation table which I built from wood.