usually they will ask the owner for the receipt, so if you have the receipt, and base on the purchase date is still within warranty period when the camera send in for repair, they will honour the warranty.
and camera store will write down the serial number of camera on the receipt.
if owner not able to provide receipt, they will take it as warranty period is over, service charge will apply. unless the model of this camera is extremely new, like release to the market for less than a year (provided it is a local set).
but the service centre able to find out when is this camera being delivered to the camera store, so they give and take a date for the camera being sold, somewhere before the next batch of same models of cameras delivered to the same store. Make sense?
However, as a show of good faith, the service center might honor the warranty (if it was not expired) if you can produce proof (receipt) of the purchase... also the second hand set must be a Local set (which mean the product is bought from an authorized local company in Singapore by the original owner). Do note that there are grey sets floating around in Singapore too, these sets normally do not have any warranty (or at the most, they have shop warranty) and so even if you bring the set down to service center and show receipt of the set, they will still not honor the warranty.
That is also why, we always ask people to check, double check, triple check, in detail of second hand product you wanted to buy to save yourself the hassle of getting a damaged product, and wondering if you can get it serviced in the service center for free...
ask the seller for the original or a copy. I don't recall Nikon having any sort of warranty registration requirement so I doubt u can call Nikon to verify anything. Not all receipts have serial numbers but the serial number on the Nikon warranty card should match what's on the camera body.
Honestly if it's your 1st time? Just save a bit more and buy new. Buying used involves risk which I'm not sure if you're ready yet.
Or get someone u trust to check the second hand set for u. Do note that sometime second hand sets might be priced too high .. So you need to do some homework to make sure you are buying at a fair price.
My first camera system I bought it new.