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.