Remember that a plane is two dimensional. You may want to extrude faces near the edge of the plane to give the impression of something substantial.

I imagine you can use the cloth feature on Maya if you have it, but if not the traditional way is to make the object (ie the cape) into a soft body in the dynamics module. I imagine you could also bind the cape to a series of joints, but I've never tried that.

Your best bet is probably the soft bodies route!

Have fun!