Thousand Islands are apparently very picturesque but there seems to be very little information on how to explore them other than a few cruise companies found via Google.
How does one visit the islands starting on the Canadian without owning a boat?
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There are a number of ways of exploring the Thousand Islands. Obviously if you own or can borrow a boat of some kind that is one of the best, but there are plenty of others. The islands come in several kinds. The bigger islands are kilometres across. They are accessible by car ferry you can just drive over and explore. The smaller ones are mostly privately owned, so you can boat round them but not land. A few of the smaller ones are owned by Thousand Islands National Park and have public access.
The simplest way to see them is to take one of the boat cruises that operate daily in season. Most operate out of Gananoque, but I believe there are others also. They will give you several hours of touring the high points. Most of them just cruise round the islands, but some will let you stop and explore select islands with public access.
You can also take organized kayak tours out of Gananoque and Kingston. These can be simple day trips for beginners or longer tours. The Admiralty Islands at the western end allow camping, so you can take multi-day tours, or just rent a kayak and go off and do your own thing. Thousand Island Kayaking will also organize a boat shuttle for you if you don't want to paddle to the islands.
Is you want a little more luxury you can also rent a houseboat in the area. The only qualification you will need to rent one is the Ontario boat operators card, which is fairly easy to get.