Right off the bat, the book you want is Carman Miller's Painting the Map Red: Canada and the South African War 1899-1902 (Montreal: McGill's / Canadian War Museum, 2002). Miller is the authority on Canada and the war, so you can follow his citations to most anything even though the book is designed to be broad and appeal to a general audience in a lot of ways.

That said, Canadians "signed up" in a few different ways. As pointed out by /u/mischiefinnbar, anti-war (and pro-Boer, not always the same thing) sentiment was far higher among French Canadians than English Canadians (and indeed there were riots in Montreal among university students over this), but the military contingent was volunteer. Canada agreed, via PM Laurier, to send volunteers to aid the war effort; Lord Strathcona helped to pay for some of them, who became Strathcona's Horse. That sidestepped the issue of making official declarations, and defused some of the public acrimony. Only about 7,500 actually went as the official Canadian contingent, making it a very small part of the overall manpower. Motivations for the volunteers were all over the place as a result, and some were new recruits while others seconded out of Canadian military forces.

There is however a second, more shadowy Canadian presence in the war, namely the South African Constabulary and its auxiliaries. See, during the guerrilla phase of the war (as well described by Miller and others like Fransjohan Pretorius), the British tried to entice more volunteers out to serve under a unified imperial South African command as garrisons at blockhouses or other key points. They did so by promising aid in settlement, which attracted not a few struggling Canadians and others (always white) from the Empire to serve there. The numbers aren't clear--they may come up in the command papers and reports about the settlement schemes--and they're not usually tallied by origin because they volunteered for an imperial venture of uncertain position in the chain of command beyond "answering to the military governor, Pretoria." Some of them seem to have stayed (one diary I saw involved a Newfie marrying a Boer widow after the war), but many decided it wasn't worth the trouble as the war dragged on, and some at least (based on memoirs in private hands I've seen) died of typhoid fever and other water-borne illnesses, because they shipped drinking water in from Johannesburg and it was of exceedingly poor quality. I'm trying now to get one of our students to dig more deeply into this lesser-known contingent of imperial forces in the war, but it's like chasing a ghost. But in that case, at least, they signed up to get land and perhaps a better livelihood than they enjoyed in Canada.

[edit: In part see House of Commons Command Paper Cd. 626, the Report of the Lands Settlement Commission in 1900 which may include some of the raw information on the latter segment.]