Mortised hinges provide a cleaner, more professional look to a door or cabinet and actually add strength to the hinge since it is embedded into the wood. Mortised hinges are less likely to twist out of place from the door's weight. A template makes cutting mortises for hinges a much simpler job than trying to chisel them out by hand.
Place the hinge you will be installing on the 3/4" plywood as if it were to be mounted there. The hinge barrel should contact the edge of the plywood and the flat hinge itself should extend across the face of the plywood. Use plywood for the template because it is both flat and stable.
Trace the outline of the hinge onto the plywood and also make a line at the center point of the hinge. This center point line will help with alignment of the template when you are ready to cut the mortise.
Set the height of the table saw to 1/8" taller than the outline you just made. This will compensate for the guide bushing needed on the router bit that will cut the mortise.
Cut out the wood with a table saw between the outline marks, extending your cuts about 1/8" beyond the tracing marks to allow clearance for the guide bushing. Usually, this is the width of a saw blade. Cut the two outside lines first then nibble away the material between these two cuts with multiple passes through the table saw. The result should be a rectangular opening that is 1/8" wider than the hinge on all three sides. Be sure to use your saw's miter gauge to make the cuts and keep your hands well away from the table saw blade.
Mount the hardwood board at a right angle to the plywood and on the same edge as the cutout you just made. Be sure to flush up the edge of the hardwood board with the plywood. Use drywall screws to secure the two pieces of wood together. This board will add stability to the template and provide a means of clamping the template to the workpiece.
Each hinge style will likely need its own template. Since this template was made over-sized to help support the router base, you can cut three other hinge templates, one on each remaining side of the board if needed.
The 1/8" cut in Steps 3 and 4 assumes a 3/4" guide bushing and a 1/2" router bit. Some woodworkers prefer a 5/8" bushing. If this is what you use, decrease the cut to 1/16" and lower the table saw blade 1/16" as well.
Be sure to wear safety glasses when working with power tools.