What do you use to attach gum paste figures to the side of a fondant cake so they don't slide?

As long as they are not too heavy you could just use gumglue..this is a little bit of gumpaste disolved into warm water till it's a glue consistancy. It dries fairly quickly and you don't need much to hold your decoration. If it's really heavy then I'd use royal icing. It dries quickly and strong.

Cat

I always like to use royal icing. Even if the figures are light, they can be bumped or shifted. I've just always found that royal icing works the best, although I have used gumglue before when in a pinch.

I like to bore a toothpick and when its dry the toothpick with a little gumpaste glue on the tip hold on to the side secure.