When you insure your car, if you are stopping with your same insurer, when they send you a quote they should say how many years no-claims you have, in the paper work.
If you decide to change your insurance company, the insurance company you were with previously, will send you details of how many years you have no-claims.
For instance I had car insurance with Saga up to 30th October 2015, their new quote I would not accept, so I changed to Hastings Direct, which was exactly £50 cheaper for the year.
Saga car insurance then sent me a letter confirming that I had 12 years no-claims protection, to which I had already told Hastings Direct.
There is a national register for car insurers, when you insure your car they check the register, to confirm anything regarding car insurance policies, to check any previous claims etc about the person being insured.