Well, in the event window, (Press F7 in the Maker to get to the event layer, then double click a square where you want the character to start as default) go to Movement Type. You can either make it random, or set a pre-set course. You can also make it go vertically, horizontally, or approach/run away from the hero. Hope that helps.
And the speed, what he said. I'd rather not use the random, since the character might walk into a door, or outside of the map without disappearing.