It's obvious how to sew one-holed or two-holed tori. This page treats the three-holed torus.
A one-holed torus arises by identifying a rectangle's sides, a two-holed torus arises by identifying an octagon's sides. Then it's not surprising that a three-holed torus arises by identifying a dodecagon's sides in the following way.
The used tools:
Construct (or draw) and then cut the dodecagon:
A lot of sewing has to be done but after the first hole ...
... it's a short way to the three-holed cloth torus:
For friends of jpegs: the little 3-holed-cloth-torus-gallery.