A "mortise" is a rectangular slot cut into wood that a corresponding piece of wood called a "tenon," fits into. A mortise has to be almost perfect for the tenon to fit properly. You can't cut a mortise accurately without some type of jig to guide your router. It's easy to make a small jig that you can use over and over for typical mortise cuts. By making and using the same jig over and over, you can ensure the consistency of the mortise cuts you make.
Drill a hole in the centre of the hardboard using the cordless drill. The hole does not have to be perfectly centred. Using a ruler and a pencil, draw out a rectangular slot around the hole. Make its measurements 1 inch-wide and 2 1/2-inches long.
Clamp the hardboard to a worktable. Insert the blade of the jigsaw into the hole that you drilled and cut out the slot but, leave just enough of the pencil line so you can see it. File the remaining edges of the slot smooth and straight to the pencil line by using the file. You should now be looking at a mortise jig, 4-by-8 inches, with a rectangular slot in the centre 1-inch wide and 2 1/2-inches wide
Clamp the jig to a sample piece of wood using one hand-clamp on both ends of the jig. Install a 1/2-inch cutter bit into the router. Install a 1/2-inch guide bushing into the router's base. The bit should penetrate through the bottom of the bushing. Set the depth of cut on the router bit to "3/4 inch."
Turn on the router and gently ease it down into the slot until it bottoms out. Using the bushing on the bottom of the router, slide it along the slot, cutting away all the wood until the wood is completely gone inside the mortise jig.
Take off the clamps. Measure your mortise. You should have a mortise that is 3/4-inch wide, 2-inches long and 1/2-inch deep. This is how big you should make your tenon.
If your mortise is not big enough or is not consistent, use the file to file away any inconsistencies, make the jig wider and test it again until its what you want. These are examples only. You can make your mortise slot any size you want.
There are different sizes of router base bushings, but typically they have the same spacings. if your jig doesn't measure up, check to see if you have an odd size bushing. If so, exchange it for a different one.