Vibration reduction:
It surrounds one of the lens elements and consists of a pair of solenoids and a bunch of electronics – as far as I can detemine from the photos – here 

What does the VR mechanism cost?
For a difference comparision:
70-300 from 1998 without VR weighs 425 grams and contains 13 elements in 9 groups.
In 2006 it was upgraded into a version with almost the double weight; 745 grams also adding VR, but I believe most of that must have been due to the change to 17 elements (in 12 groups).
An attempt at analyzing: The difference is 320 grams in four elements,  count VR as one element; then the difference is 320/4 = 80 grams average per element.
Due to the fact that it is easier to move a light-weight object (one of those lens elements) I have hard to believe that the VR-element is one of the bulkier (check the images under the link above). So, this leads to a conclusion that the weight addition is less than 80 grams, at least for the 70-300 VR lens. 

Price difference is harder to compare; the older versions of this lens has a price around $100-$150 on New and refurbished VR-versions starts at $500-ish.
The difference of $400 is hardly due to VR only; the VR-version of this lens is a bargain and a true performer on DX, and fairly good on FX too as far as I know (softer corners).
Might I guess that VR adds $100-125 to the cost of a a lens?  (Note: DX 55-200 VR is just $200+). 

The 24-70/2.8 weighs in at ~ 900 g (31.7 oz, 15 elements/11 groups) and the DX 17-55/2.8 at 755g (14/10), the difference would hardly be noticeable would they have VR added. 

What difference does it make then?
The way Nikon tells it is here.
In practice:  Most people recognize the usefulness at long focal lengths, not many are aware of the benefits at short focal lengths though…
The more reasonably tagged (price) DX 16-85 VR weighs 485g (17/11),  is one of the lenses I happen to own.
With this lens I handhold the D300 at shutter speeds of 1 second (about 50% success), longer is harder – but  will often succeed with the help of support of some kind.
If I turn up the ISO to Hi1.0 (3200) in P-mode, the camera still thinks the same subject is “Lo” (underexposure). 

Quick examples: Click on the image for a 4MP size crop from the original, which was munched into 1.5MP by wordpress at upload (maybe I should make an effort to create better examples, “real soon now”). NOTE: The first image is a crop of the thing straight out of the camera, the second one is an edited version of the same.
Also: – 1/4s exposure at 300mm (equiv to 450mm for FX!).

2010-03-09_17h39m16s_ND300-2253.nef (4MP crop from the middle), NIKON D300, 1s, ISO 200, -5/2 EV, 16-85mm f/3.5-5.6/AF-S DX VR Zoom-Nikkor 16-85mm f/3.5-5.6G ED @f/3.5, 16.0 mm (35 mm equivalent: 24.0 mm)
One second exposure, quickly edited state.