The range hood and the vent kit will both have instructions on how to install them. It has been my experience that the instructions are either poorly diagrammed or make some assumptions on your ability to improvise.
I am not going to tell you a different set of instructions but provide some things to consider that might make the task of installing both the range hood and the vent kit (the part that goes outside) a bit easier. AND help ensure the two match up.
CAVEAT: The tips I provide here relate only to the straight vent approach - that is thorough the wall.
1) Assemble and dry fit the range hood
Make sure all the pieces at there. Actually install the hood and then mark the hole at the back of the range hood on the wall.
2) Drill four pilot holes
Using the hole you marked on the inside wall (in the first tip above) drill a hole at each of the four corners with a 1/4-inch bit that is as long as your wall is thick. This will likely mean you will need to get a drill bit that is approaching 1-foot in length. Drill these holes as level vertically and horizontally as you can manage.
3) Measure the box on the outside
Ensure the box, on the outside wall, now defined by the four holes you drilled above, have the same dimensions as the inside 'box'. Adjust accordingly.
4) Create the vent hole
Carefully cut the hole in the wall. Use a drywall saw on the inside and a jig saw on the outside wall. Take out only enough insulation in the wall to free the hole.
5) Be prepared to make your own wall tube
Make sure you have some sheet metal on hand to fashion a square tube in the wall. I disoverd that neither the range hood nor the vent kit I purchased were long enough to joint up. Also make sure you have duct tape to seal up all the cracks - we do not want all that bacon grease blowing inside the insulation.
6) Securing and sealing
Make sure you have at least 4 stainless steel screws to secure the vent kit on the outside. two and half inches in length should be long enough to bite in to the wall through the outside covering (like siding). And do not forget to caulk on the outside.