I would like to put a convection microwave oven over the counter and above my dishwasher so that I have counter-space that is clear for working. How would I attach the oven to the wall - it is an exterior wall.
The normal way to handle this would be to put the oven inside a cabinet. Many nicer microwaves also have an option of purchasing a "trim kit" that will make it look like a nice, built in wall oven, but as long as you follow the specs for side and top clearance, just an open box of a cabinet will be fine.
The other option would be to just install a shelf for it to set on, but you would have exposed shelf brackets. A cabinet would be held onto the wall with internal fasteners, and really is the "correct" way to handle this.
As far as mounting it directly to the wall, some microwaves are meant to go over a stove, and will come with a mounting bracket for the wall, but they also assume there will be a cabinet above the microwave to carry most of the weight.
You also need to consider where the microwave will be plugged in. You probably need to add another outlet, but that's a different question.
Here are a few links for typical installation documents that you need to look for when picking out a microwave: