This answer is based on a 17-foot plastic Coleman canoe with an aluminium frame. The length and the plastic increase the challenges. I have over 100 miles experience now, with legs of 14 to 15 miles.
After much online research I purchased a Seattle Sports All Terrain Canoe Center Cart; there is an option that includes a tow bar to connect it to your bike, but that is for a max of 16 foot canoe. The Seattle sports hitch is a low mount hitch; most of the home made solutions you find on Google are high mount: see What are the safety concerns of a high vs a low mount trailer hitch?
Pretty much all the commercially available carts are designed with a couple of padded rest points that your canoe or kayak will rest on. This might be OK for short distances or with an empty hard-shell (fiberglass type) boat with nothing in it, but for a relatively soft plastic canoe, loaded with gear, traveling more then a mile or so, in warm (or hot) weather, the issues start to build up.
Problem one: a trailer hitch. See Trailer connection, off the shelf parts and proven performer, for my solution.
Problem two: keep the canoe on the cart. The strap that comes with dolly is not going to work, I tried several variations and a single strap is problematic for any distance. Every time you hit a pothole the dolly moves a bit. Pretty soon the dolly has slid back and is partly sideways; your 3-foot wide canoe is making a 5-foot wide swath behind you. I tipped the canoe over on my first outing, brushing against a pole, had to stop every mile and recenter it.
Solution is four straps; the image shows 5, but the center strap turned out not to be required (and is more likely to wear (break) when you brush against things. Two straps pulling the dolly back and center, two straps pulling the dolly forward and center. I used 15-foot ratchet straps in the front, and wrapped around the trailer hitch before hooking to the seat. You don't need much pressure; it just needs to be snug.
Problem three:The plastic hull is resting on the padded bars of the cart; this was okay at first, but the warm weather and time started causing the canoe to be come deformed. I tried using a strap between the bars for the keel to rest on, but I started to notice the canoe rubbing on the cart wheels (and damaging the canoe).
Solution build a wood deck on the dolly. There is a space for the keel; now most of the weight is carried by the keel. The large flat area (shaped to minimize pressure points) provides balance and are helps to reshape the hull. It is easier to get and keep the boat centered on the cart. This added a couple of pounds, but it has been more then worth it. The canoe can't rub against the tires. I actually picked up about 2 miles per hour on the first outing with the wood deck.
Although not shown on any of the images above, I also used a bungee cord to support/lift the hitch a way up the seat post. Without it the hitch would occasionally drag on the rear tire.
Pulling the Canoe
Actually towing the canoe is not as bad as I had expected.
It is heavy, and the cart tires are relatively wide. Racing bikes have skinny tires for a reason: less friction. Here, I have all terrain tires on the bike and the canoe dolly. All of which means it is harder to go fast. It also means you go over rough terrain easier and have more control, so it is trade-off.
It is long, I mean really long. The national move yourself trailer rental company (US) does not even rent a trailer as long as the canoe. AND because the dolly is in the center of the canoe, it pivots in the center of the canoe when you turn. When taking a sharp corner the back of the canoe can swing out 8½ feet (nearly 3 meters): if you are on the center line of a road, and turn sharp, the canoe could hit a car parked on the side of the road. I recommend you practise turning, well away from things that might get damaged (e.g. in an empty parking lot).
With some practice, you can tow on roads without difficulty and on most areas of bike paths fine. Slow down for corners; get off and walk everything around narrow corners. Sometimes the bike must be carried or disconnected from the canoe to make it through tight corners or narrow areas.
My canoe is about 3 feet (1 meter) wide; many bike paths in the US have posts to prevent motor vehicles from going on the path, These seem to mostly have about 3½ to 4 feet of space between them so the canoe does fit. You will want to walk through while learning but now I am able to bike through about 95% of them. Get lined up well before you get to the posts and don't turn until the entire canoe is through (the tail will swing and hit a post).
Expect the canoe to rub in tight spots even if you are moving it by hand; bring extra straps to connect it to the dolly.
Use extreme cation when corning if there are people, cars or anything damageable around.