How do I cook a frozen hamburger in the microwave?
I don't endorse beef in the microwave, but that said, the best possible way to cook it is going to be on one of the microwave plates that raise your food off the plate. (the ones that look like the inside of a george foreman grill)  You are going to have to play with your power settings a bit to achieve a optimium patty.  In mine, it's 2:30 at 40 percent power and 1:30 at full power but depending on wattage, your particular times are going to vary.

The trick to having an edible patty come out of the microwave is use low power to achieve the desired temp and then hit it at full power to get the outside done.  It will always produce a slimy-er patty than cooking it on a stovetop or in an oven.  Make sure that you cover the patty during cooking as it is going to spatter like crazy.  You don't want to clean that mess up.

If you have access to a toaster oven, you can cook a patty in that in about 15 minutes and you will have a much closer to delicious product.