This is a basic technique if you want to cut rectangular openings.
Utilize it if you want to handcut wall openings or - like I did - door frames.

Rectangular Openings

Mark the opening on the wood with a pencil. Then follow the lines with a craft knife or other sharp tool and make a notch. This helps to get a straight cut later.

Now drill a hole into the section that will be cut away. It shouldn't touch the line, but make it quite close to it.
Loosen one end of you handsaw's blade. Insert your blade through the hole and refix the blade.

Now cut along the lines. Try to make a straight cut - but don't worry: I learned that even more experienced people sometimes make crooked cuts with a handsaw!
Leave the corners for later, for now just cut a bow as narrow as your blade allows.

Now you have the space you need for cutting exact corners. Just cut from both sides into each corner until you reach the point where the lines meet.
Unassemble your saw again in order to take out the blade.
Sand the rims of your new opening. You get a straighter edge if you wrap your sandpaper around some straight piece of wood while you do this.

I did not invent this technique. One person who taught this, is Beryl Armstrong.
(Look at my sources page for details on her books).
I just thought I might present it here, since I had those door-pictures handy.