The best spot (and perhaps the only one) to hitchhike to Munich is on the Memmingen-Ost on-ramp, situated at the edge of town. To get there walk from the center on the Münchner Str. for 1 kilometer till you reach the on-ramp. Then turn right where the traffic turns for direction of München, and hitchhike there while standing on the grass on the side. There is not a great place for the cars to stop, but they can always stop on the grass or stop for a second on the road if there is not much traffic. It's best to hold a M for Munich or AU for Augsburg sign.
From the airport you should use the same spot, it's only a bit more to walk (around 2.5km).