Well, there are a few ways you can do it:
Firstly, attach a small magnet to the bottom of each leg on the armature and then place it on a magnetic surface. This will add weight to stabilise your character and means that it will stand freely far easier.
You can also use tie downs, which entails putting a bolt in the foot of your character and having holes across the entirety of your set. This way is obviously very impractical and usually ruins a very nice set.
Finally, you can make a character walk without even making them leave the ground! Sounds ridiculous I know, however, it works, and does so very well!
Here is an image Cavor posted some time ago (It was pretty arduous task going through my animation/sculpture folder to find this image hehe) showing how to get an effective walk cycle without your character leaving the ground.
I hope this gives you a clearer view on how to get a decent looking walk cycle when animating. If you have anymore questions I'll be here to answer them as well!
Good luck,
Joshy666