I have a friend whom I can refer about this procedure.
http://www.mayoclinic.com/health/deep-brain-stimulation/MY00...
The one traumatic part of it is that some groups use a device popularized by some of the French groups that use a 5-microelectrode array for the mapping portion of the surgery, which has a 4x4 cross sectional spread. This probably pins and destroys a lot of the brain tissue in its path, but the people who use it claim it gives them "better spatial resolution" in the mapping recordings. Which doesn't apparently improve overall accuracy anyway, but some people are married to using that damn device.
Most surgeons in the US use 1-3 single electrode passes sequentially, which is a lot better.
So the usual caveats apply. You need to have tried other means (pharmacological, exercise), need to be healthy and willing to risk adverse consequences. In the case of the video linked, it is somewhat of a no brainer. The person is young 39 years old with a family. He seems to have a pretty bad case of Parkinsons. I'm sure he is willing to enjoy a much better quality of life even if it is risky.
They're trying to do some sort of closed loop feedback instead of some clinician inputting random settings of volts/frequency/pulse width into the device, but no one knows exactly what signals in the brain to listen for yet. The EE-oriented neuro types are looking at signal processing, i.e. using FFT's to look at power spectra of local recordings, etc, but nothing too promising yet.
As far as what the physiologic mechanism of the electrical stimulation does, no one really knows, but there's some data from monkeys and mice optogenetics suggesting it activates passing axonal fibers. Generally, nerves don't die due to the electricity, unless your surgeon does the implant French-style and shoves a 5-microelectrode array into your head, therefore boring a nice 2-4mm tunnel into your brain...
Otherwise, the most common side effects that could happen is that the stimulation causes some spasms or tingling. There's some hand-waving as to whether it may increase susceptibility to depression or falls, but that is hard to tease out between disease progression.
Of note, if it's Parkinson's, one hard part is that the meds will have to be adjusted a lot post-op which cause some folks problems.