[UPDATE: thanks to Zephyris, which has reminded me with his good Instructable that you first have to reverse one of the two CPL filters, of course I've found his Instructable shortly after publish mine, as often happens to me, and in this case I've also forgotten I already commented his instructable two years ago...]

A Neutral Density (ND) filter is a cool gadget, you should always carry it (at least daytime). You can find easily ND2, ND4, ND8 filters, these would darken your scene of 1, 2 or 3 stops respectively. When daylight is very strong it's difficult to keep a very large aperture, so you couldn't have low deep of field or nice bokeh. In these cases an ND filter should be very useful. I also use it to keep very long exposures in daytime. You can obtain unique effects, with cars and people moving as ghosts.
Of course you'll reach a better quality with traditional ND filters, but if you have two polarized filters you can experiment a really funny phenomenon. I suggest circular polarized filters (CPL) rather than linear ones, because with CPL you can keep automatic focus of your camera, whichever is the rotation angle of the filter on the lens. You can buy CPL filters on eBay, or at your favourite photography shop, you can find every diameter.

Step 1: Taking a Closer Look

Polarized filters could rotate, so when you screw them one to each other, you could turn them mutually obtaining to let pass through all the light or block it, and also every step between two positions. This happens because light is normally formed by waves lying on various planes, and each polarized filter blocks all waves except ones on a typical plane. If you have two perpendicular filters the second would stop this wave too, and no light should pass. If the filters are aligned, all light which has passed through the first should be already on the right plane to pass in the second too. It's as making a toast pass through two barbeque grids...
Actually this is right for linear polarized, but for CPL is slightly different, and very difficult to explain. Anyway the idea at the base of this Instructable is the same.

Step 2: Making the Tools

With CPL filters you have to reverse one of the filters. To know which is the right orientation of a CPL filter you could look at your PC monitor through it, and if monitor changes luminosity rotating the filter, the orientation is right, if it slightly changes colour so the filter is reversed. For our Variable ND Filter you need to dismount a CPL and reverse the glass. To dismount it, as I already explained in the other mandarin Instructable, I've built a pair of tools.

Step 3: Some Test

Now you could screw up the reversed CPL filter over the original one, so that this last remains on the camera side, and the modified one stays outside. Then you can test your filter on a normal light source. You see very well the variable ND filter behavior in these images. Filters are aligned in first photo, and they're perpendicular in second one, where no toast would pass through the grids... nope! no light would pass through the glasses!

Step 4: To the Extreme!

You'll run probably in strange unexpected effects if you'll photograph sky with perpendicular filters... because a little of light is still passing, and you could capture it with long exposure times. If the filters' polarizations are not perfectly balanced you'll probably obtain something as in this my photo, where you see a strange blue X shape. Details of the shot are: 200 ISO, 1/30 s. and 4.5 aperture.

Step 5: The Results

Now you can test your new Variable ND Filter directly over the clouds. Beware to not point directly to the sun before setting the filter to darken position, to avoid burn your sensor. This is my test photo, compared to the one without filter to compare image quality. Note how the shutter time of the first photo is much longer than second, despite aperture is wider. First day of sun I'll make some more interesting photo to show you ND filter behavior in a crowded "piazza".
And yes, I love mandarins! ;-)

UPDATE:
Dear followers, give a look at my Picasa Gallery to see last photos in Milan to test filter.