Kingston is located half-way between Toronto and Montreal, on the shore of Lake Ontario (one of the Great Lakes). One can only fly to Kingston via Toronto Pearson International Airport. Unfortunately, the short flights between Kingston and Toronto tend to be unreliable at best.
The best way to reach Kingston is to fly to Montreal Pierre Elliott Trudeau International Airport, take the free VIA shuttle to the Dorval VIA train station (which is only a few minutes drive away) and take a VIA train to Kingston.
See VIA Rail Canada: Train travel in Canada for information about the VIA Rail service.
Alternatively, one can fly to Toronto Pearson International Airport and take the UP Express train (not free however) down to Union train station in downtown Toronto and then take a VIA train to Kingston.
See UP Express | Pearson Airport to Downtown Toronto in 25 minutes for information about the UP Express train service.