If the VOR is an "overfly" fix, for instance as part of an approach procedure, you should not anticipate the turn, but rather initiate the turn right after passing the turn. Obviously you've now overshot the new radial, so you need to turn a bit more to setup an interception course - typically 30 degrees or so.
If you are allowed to anticipate the turn, here's what I do. You calculate the heading change, and calculate how much time such a heading change is going to take, assuming a rate 1 turn. So if I need to turn by 100 degrees (per your example), it will take 33 seconds (3 degrees per second). I then anticipate the turning point by starting my turn half of this number of seconds early. In this example, 16 seconds before I overfly the VOR. If necessary, you can convert this into a distance if you know the groundspeed, but most DMEs will actually do this for you already.
For relatively shallow turns, up to approximately 90 degrees, this works a treat. For turns significantly more than 90 degrees you've got to start the turn a lot earlier in order to end up on the proper outbound radial. There are better methods for calculating that, but they're more complex and not as easy to remember.
And in any case you have to take slant distance into account. If you're at about 3000', directly over the VOR/DME, the DME will show 0.5 nm, not zero. A GPS makes this a lot easier, and a moving map GPS even more so.