You know that purplish glow you get when you use a blacklight bulb normally? A small amount of visible light will also make its way into your photos using this DIY method. Many UV photographers choose to keep this in their photos, though others prefer to adjust the colors with some photo editing software, or have a custom white balance for their UV photography.
Since blacklight bulbs use Wood's Glass, there will also be a small amount of IR light passing through to your camera lens—so, if you want to be improving the “UVness” of your shots, then adding in some sort of IR blocking filter will help things along. A major source of IR radiation is the Sun - so if you don't shoot during the day and use another blacklight bulb to light the scene, you can further improve performance.
Nor does will this capture the full range of UV radiation—as you might have guessed, only the wavelengths that are closer to that of visible light. Only the most expensive of filters can capture anything close to the full range, and even then, that requires extremely specialized equipment.
Also, many modern lenses block a good deal of UV light already in having built-in UV filters (which will obviously block the UV light you're trying to isolate.) So, if this doesn't work for your camera, try it with a friend's camera. Don't make great demands of sensitivity, either: this is a rough DIY trying to approximate a very specialized and difficult technique.
Otherwise, if all goes well, you'll be exploring a whole new world of light that just isn't visible to the naked eye—all through the lens of your camera.
For the inspiration for this article, in addition to some sample pictures, check out this Instructables article.