Wikipedia talks about dredging existing waterways, which I suppose I can see being done with relatively simple boats. But what about canals that were wholly new waterways? How were they dug once they were deep enough to be before the water table, without modern pumps? Lots of muscle power, or were there more sophisticated techniques at work?
A lot of man power, often in the form of navvies, who are actually named after their work on the canals - naval engineers.
The average navvie could dig a trench 4 foot wide, 4 foot deep, and 30 foot long in a day. And lift it all above their head.
Hire enough people, and you can build anything big enough.
Liz McIvor did a wonderful series of documentaries for BBC 4 recently called 'Canals: the making of a nation' which is greater starter point for ho w the both built and designed canals, even down to the history of the materials used.