This is pretty easy if you have the proper tools and assuming that a very slight curve in each corner is acceptable.
1. Layout your rectangle on the workpiece
2. Measure in from each side by 1/8" (or less depending on how good you are with measurements and stuff) and make another "interior rectangle." Now in each corner you should have a reference point that is 1/8" in from the sides
3. Using a 1/4" drill bit, drill out the 4 corners using the interior rectangle points as the center of the drill bit. It helps to use a nail or screw to make an indentation on the point dso the bit does not slip.
4. Using a jigsaw, freehand the rest of the rectangle staying about 1/8"-1/4" from the line which will remove the bulk of the material.
5. Using a straight edge, some clamps (to hold the straightedge in place) and your router with a pattern making bit, remove the excess material exactly on the line (you have to do this for each side)
6. Use a chisel if you really want to square up the corners but you probably don't have to.
I detail how to do this with pics
HERE - I just cut out my coin door (so my rounded corners were a little severe) but the process is exactly the same. Also check out
HERE for detailed pictures of setting up the router and straight edge - actually, in this post I cut out a perfect rectangle. Hope this helps.