Installing a microwave oven in place of a range hood is a common upgrade. Not only is it very convenient, but it clears some space on your countertop.
If there is currently a range hood in place, then there is already power in the cabinet above it. So it is a matter of removing the range hood and installing the microwave. Unplug the range hood and look below the hood. It will be held in place with four screws. The hood will drop down and as you remove it, thread the power cord through the hole in the underside of the cabinet and remove it.
The microwave will be considerably heavier. It is held in place by a bracket that is screwed to the wall. The key here is that at least one of the screws that hold the bracket to the wall must be in a wall stud. The others can be held with wall anchors (check with the manufacturer for the specifics). You will need to attach the cord to the unit and thread it through the hole where the old one went. Lift the microwave up and set it on the lip at the bottom of the bracket and then swing it up into place. You will install a screw through the cabinet bottom that mates with a hole in the top of the microwave (there is a template included in the box to mark the location). As you tighten the screw, the front of the microwave will rise up to meet the bottom of the cabinet.
By the way, microwaves are set up to recirculate the air back into the room through a charcoal filter. You can install it this way, or if the microwave is on an exterior wall, you can rotate the motor 90-degrees and run the venting up and out of the house.