I'm often asked by glassblowers who shoots my work (me) and advice for photographing glass. Instead of replying by email each time, I'm going to summarize my setup and advice here so it's easy to reference. I've been a photo hobbyist for years and since I initially got into photography by shooting underwater (which is more technically demanding) I had to learn basic photo concepts and tools. However, with just a little investment in learning about photography and a homemade setup, you can still get really good shots of your glass.
My setup is pretty simple, but specific. Since most of photography is all about lighting, I recommend getting a book on studio lighting like this one so you can learn about light, tools to adjust it and exposure to get what you want.
I made my own large shooting table somewhat similar to this one because my work can be tall and heavy and I could make the frame and purchase the acrylic making a large custom setup for a fraction of the cost of buying one. I made my table out of square steel tube to hold a full 4' x 8' sheet of clear matte acrylic (p95 matte finish) for a non-reflective surface, backed by a thin sheet of translucent neutral white acrylic for light diffusion and a seamless white background.
I light work two ways: from the underneath/back and overhead. The backlight is underneath the table and shines directly up--I arrange the light so it hits just behind the piece. It lights up transparent sections of glass and creates a halo around the top of the piece. I fire this up and move it around to get the effect I need before I turn on the overhead light which is in front of the work but at a high angle pointing down. If you light directly over the piece you'll get rough shadows and the front of the work will be dark. If you light too far in front of the piece you'll get hot spots and bad shadows on the background behind the glass. My light is probably about 4' above the work and 1.5' in front of it. The two lights I use are Lowel Pro-Lights with barn doors so I can shape where I want the light. They are a bit pricey new but can be found used on eBay and Craigslist for something like $70 each. I don't diffuse the light because it creates larger hot spots and I want a sharper falloff and fade to grey/black versus an even light level.
After shooting I edit gently in Aperture to make sure the image matches the work. I generally straighten, crop to size, sharpen to remove softness and blend any harsh shadows that are on the background. If you have a Mac, Aperture is great for easy light editing like this. You could also use Photoshop, Lightroom or many other applications for this type of minimal editing.
I shoot with a Canon 40D on a manfrotto tripod and use a circular polarizer to minimize reflections off the glass and the table. I shoot in manual mode at F11 since that's the sweet spot for the lens I'm using and auto bracket so I'm assured of getting a good exposure. I shoot in mirror lockup mode with a remote shutter release to minimize vibration since my exposures are frequently half a second or more. Although pro photographers will scoff, I admit I shoot high resolution JPEGs rather than raw since I'm sensitive to the time it will take to process raw files and the space that years of raw images plus the resulting jpegs will occupy up on my laptop's drive.
I evolved my setup to what I've described above as my needs changed and my own standards for image quality grew. But you don't need a fancy camera or custom table to get good results. You can get decent images with a shooting table made from 2x2s with a glass platform and seamless paper backdrop draped over it. I used clip lights from home depot with halogen spots for years, using cinefoil around the shade to to shape the light. If you have a DSLR great, but even if you're using a compact, set it for the highest resolution image, use the custom white balance setting, mount it on a tripod and try shooting in either auto with the flash off or aperture priority so you can set the aperture small enough to have good depth of field. If your camera will accept a circular polarizer, definitely use one but remember that you need to turn it to find the right setting.
Hope this helps in getting good shots of your glass!