There are many versions of the tapering jig. I have one that I made several years ago that I’ve used for various projects (stair railing rebuild, for example). It’s an improvement on the classic design, in that the body of it is wide enough to let the stay slip over it. Also, the wide body made it so that the stay could be straight, rather than curved, like on commercial designs. Having the body wider also puts more distance between your hand and the blade when you are pushing it. Simple and effective, it works well but the design can be improved upon.

I get started with a piece of 1/2″ plywood, cut 30″ long and 6″ wide that will be the base:

The quality of the plywood is fairly important, in that it should be flat and smooth. I’m using good one side pine plywood, which is very nearly void free and stays reasonably flat.
Particle board, melamine or MDF could also be used.

The end block is 3/4″ plywood with a handle hole and a slot cut into it. This is glued and screwed to the base. I then glue and screw a piece of 3/4″ thick pine to the side that runs against the fence :

This stiffens the base and also acts as the top step in the step clamp system.

The next step is added. This is 3/4″ shorter than the first and not as long. It’s just glued and clamped. The third step is then glued and clamped in place. It is 3/4″ high and just as long as the second step:

A stop block is made and a carriage bolt, washer and wing nut are installed. This is adjustable to set the taper:

For the step clamps to work, there are three different lengths of hold downs needed. I figured the chances of loosing all of these hold downs was pretty high, so I thought to make just two, that are triangular. By reorienting it, it would work on a different step. It took a little crude geometry, but I soon figured it out.
Putting my beam compass to work:

I actually worked out the dimensions in SketchUp (saved much paper and plywood, no doubt!)

I cut the triangle with my miter saw by lining up the laser with my layout lines (the angles are all “point something”, so this is the most accurate). The table saw is set to clip the tips off giving the thee lengths:

Three holes are drilled, one for each step:

A word of caution about material: these hold downs should be made with strong plywood, at least 1/2″ thick. Avoid using solid wood for these as it can split unexpectedly.

The bolts are then put in with a nut and washer on the top side. Some construction adhesive is insurance against the bolt loosening over time:

They are evenly spaced, 5″ apart:

The jig complete and ready for a test run:

I made a short video on building the tapering jig:

I figure this is a good Saturday project, easy enough to finish in one day and can probably be made from scrap material – mine was!