Polarized Material. Uh-oh. Where do we find something that's polarized? Luckily enough, there are literally hundreds of everyday objects that can be exploited for their polarized screens.
The easiest to adapt to our purposes is probably a good ol' fashion pair of 3-D glasses – each lens being polarized, just rotated at an angle to each other. (For an example of this approach, check out this YouTube movie.) Your everyday LCD screen has two sets of polarized screens in it, one on each side of the LCD itself. This will have to be removed carefully, but it can be done. Polarized sunglasses, if you can find a clear pair (or a colored pair, depending on what you want) might also work in pinch.
So, ask around if anyone has a damaged LCD screen you can salvage a corner of, or keep an eye out in those thrift stores for a cheap pair of glasses. Make sure that whatever you use is unscratched, and is large enough for your camera.
Cutting utensil. Box cutters work great, especially if you'll be working with hard materials – probably mostly plastic - and will need to make precision cuts.
Sandpaper. Smooth edges are easier to work with, so having sandpaper really helps. Failing that, a good emery board might also work.
Glue. Hot glue is probably a good bet, since you'll probably be working with plastic, though anything that's strong and won't expand too much will work just fine.
Filter Attachment. The details of how to make a DIY filter mounts are explained in this article.
A few notes specific to polarized filters: these filters tend to be the real workhorse of photography filters, so building it in a sturdy fashion – and in such a way that other filters may be used in addition to it – is really a must. You'll want something that can rotate, so simply taping it on to the end of the camera will not suffice. Being able to attach two to your camera at once allows you to do some other neat DIY tricks, such as a variable ND filter. Thus, it is recommended that simply reworking an old, damaged filter is the best solution.