What about buying one instead of building your own?
There's been a handful of cars in the last 5 years with CVT's, you could
probably find one at the junkyard or an auction, pull the CVT and scrap
the rest of the vehicle.

Probably cheaper than designing and building one from scratch, unless
that's a big part of the project.

Ray

If you are looking to use it on a low power unit then just find a junk
motor scooter.

Riding lawnmowers.

Are you a machinist? Are you a metallurgist? Can you heat treat?

buy a blown up snowmoble and use it's final drive system

No tips on constructing one, but here's the basic principle:

http://auto.howstuffworks.com/cvt2.htm

4 V-belt pulley halves and some actuators to make them open and close
in opposition to each other shouldn't be too hard to construct in a
machine shop, given enough time and money. V-belts are cheap and
plentiful, just pick one with the right V angle and width. The belt
will probably need to be quite wide to accommodate a useful range of
ratios, so you might look into V-belts designed for industrial or
agricultural applications rather than automotive.

As mentioned, a scooter is probably a good source for a small CVT.