How do I get a player to move on a grid based system?

I'm trying to make a game based on a grid. You have a stickman army and you then move them based on certain grid restrictions (2 horizontal, 1 vertical, 1 diagonal) and shoot the enemy team based on range that varies per weapon. I actually have no idea how to approach this, help please.

There's a MoveTo plugin that I used to have objects move in a grid so you can say move x+32 and it'll move right 32 pixels and stop, move y+32, it'll move down 32 pixels and stop etc.