I had Nerve Conduction tests about 4 or 5 yesrs ago. I was at the hospital for around an hour and a half. A doctor (who was doing research of some sort) asked me to lie/sit on a trolley type thing. My back was supported, so I was quite comfortable. After a short conversation about the pain I had been experiencing in my hand, he attached electrodes to my arm in different places. He explained he would pass an electrical current through them. If just felt as if my arm had received a terrific whack or jolt, coming from no particular place, but was not actually painful. He then repeated the test on one of my legs. He said this was for comparison. The feeling was similar. I was told that people's reactions vary quite a lot.
The doctor was young and quite chatty and told me he couldn't see any problem but that the results would be sent to whoever requested the tests, in my case an Orthopaedic consultant I was seeing over arthritis in my hands. I got the results officially at my next appointment in the Orthopaedic dept. If your results are going to a GP, you might get them sooner.
I've had more pleasant experiences - but it was nothing to be worried about.