She said (in comments) that she has used a towel here as a background: http://500px.com/photo/4934925
That is a macro shot.
But, the towel isn't simply "visible" (except very faintly on the right corner). Is it possible to make the towel invisible without any post processing?
For some reason I can't see the image linked above. But anyways based on what I've read from few responses I assume the towel is pure white or blown out in the background.
Here is a quick diagram to help you visualize: top view.
All you need is two lights. Set up your main light first, get the exposure you like. Then add second light that is 1 or more stops brighter than your main light. You should consider snooting second light. Snooting helps you direct light where you want it. In this case you might not want to add more light to your current exposure of your subject but you want to overexpose the background.
EDITED TO ADD: Resources
One Light DVD by Zack Arias. And Strobist (Free)
Absolutely. This effect is achieved very simply with lighting. Most likely she had a light behind the towel as well as having sufficient light in front of the towel. By setting her exposure properly she guaranteed the background would end up pure white. This is a pretty common technique.
You see it with a lot of model pictures on a white background. Those are shot with a paper roll (usually) as the background. It's the combination of setting the lights in the right place and setting the exposure properly that causes the background to go pure white.
In fact, this effect is far easier to achieve in camera than in post processing.
Edited to add that having a shallow depth of field in this shot also contributed to the background going white. The blurring effect of the aperture smooths out the texture in the properly lit background.
I believe, as some of you do, that this is primarily a "shot right" image.
I don't believe there is a light behind the towel, because there is no highlight that suggests a light source other than the front light.
It's not completely white. Really close, but not quite. This would not be sufficient for catalog work, but still makes a darn nice image. If the 1-1.5 stops difference had been achieved between foreground and background, the background would have been completely white.
The shallow depth of field, makes the blend into the background look natural and eliminates any texture of the background towel.
This is not an ideal setup for on-white shooting, as that requires good separation (distance) between the subject and background. That's why models typically stand 8-10 feet from the backdrop. If you get too close, the background becomes a light source, and a pretty significant one, making the edges look washed out where the light wraps. Still, this can be achieved in a mini-studio with some work tuning the light output and placing flags.
The question, "how many lights," is difficult to answer because so much depends on the size of the subject and the size of the backdrop. This one could have been shot with two or three low-power lights. Low power because the depth of field falloff is so dramatic.
So, if I had to shoot this, set up as it is, I would place one light in front, and one above the backdrop facing straight down with a flag to block light from going forward to the subject. A flag is just a black card designed to make sure you control where light goes. I use a strip light for this, but you can use whatever you like so long as it covers the background and doesn't spill forward onto the subject.
I can get these to nearly zero post-processing necessary, but if I need some, I use the dodge tool in Photoshop, set on highlights, at about 10% and nibble away on the areas that aren't really white. It usually takes a couple of minutes, but you have to be careful of edges because you can really mess them up if you use too heavy a hand in post.
If you love these isolated effects, you should practice them on white, on black, on gray, whatever you like until the lighting is pretty automatic. I know, it's boring once you've solved the lighting puzzle, but that leaves you free to focus on composition. The other thing is that different materials react differently to your lights. Glass, as in this image, is particularly interesting to shoot, as you need to make conscious decisions regarding whether the reflections of lights and the camera itself are acceptable.
As mentioned by nwcs it can be done by post processing easily.
Here is an example where I did the same thing. I have used a navy blue towel as a background and post processed it to make it black (mainly gamma correction in photoshop).
Let me know if you need some help to figure it out. I hope this helps.
