While there may not be 20 different ways that the English and French colonized Canada, there are at least 20 important events and incidents that were involved that should provide you with context for how it happened.
You might say that colonization officially started when (1) Jean-François de la Rocque de Sieur Roberval was made the viceroy of Canada by the French king in 1540 and given the authority to establish a French colony there.
England got officially involved when (2) Sir Humphrey Gilbert claimed Newfoundland for England in 1583.
(3) In 1598 Roberval received the first monopoly in the fur-trade. This began the first major enterprise into mercantilistic based imperialism in the region.
(4) Samuel de Champlain's founding of Montreal in 1608 and the consolidation of the Canadian colonies (5) can be considered the events that really established Canada as a viable colony for France.
(6) In 1610, John Guy founded the colony of Cupid's Bay for England. Although this colony was short-lived, it did a lot to reinforce England's claims in the region.
(7) In 1611, the first Jesuit missionaries came to New France where they successfully established a number of missions aimed at converting native peoples.
(8) The seigneurial system was established in 1623. It divided land ownership in New France in a feudal manner and would continue under English control.
(9) In 1645 the fur monopoly was transferred to everyone in the colony. This greatly encouraged more fur trappers from Europe to come to the region.
(10) Canada's first political constitution was implemented in 1647 under the Council of Quebec.
(11) In 1663, King Loius XIV revoked the charter of Compagnie des Cent-Associés making New France a colony of the French Crown.
Things heated up between England and France with (12) the founding of the Hudson Bay Company in 1670. This English monopoly took control of much of Northwest Canada and provided French fur traders with serious competition.
(13) In 1677 the first of many so-called "wampum treaties" between the English and indigenous peoples was formalized. These treaties established friendly trading relations between Europeans and many native groups.
(14) The French and Indian War (aka, the Seven Years' War) resulted in the British annexing nearly all French controlled land in Canada.
(15) After the English took control of Canada, large numbers of Scotch-Irish settle there, particularly in Novia Scotia and the Maritimes.
(16) The colonization of western Canada was firmly established in 1825 with the founding of Fort Vancouver by the Hudson Bay Company.
(17) In 1857 the government in Canada attempted its first large-scale attempt to colonize the native peoples with the establishment of The Gradual Civilization Act which required all native adult men to learn English or French and change their names.
(18) Between 1871 and 1877 a number of treaties were signed between the government and individual tribes that stripped away much of their lands in exchange for supplies and infrastructure.
(19) In 1884, native rights were further stripped away with the founding of residential schools and the proscription of indigenous ceremonies. Attending the schools became mandatory in 1920.
(20) In 1896, restrictions on foreign immigration were eased. This led to a huge influx of immigrants from southern and eastern Europe. This essentially turned Canada from predominantly English, French, and Native American into the melting pot that it would become over the course of the 20th Century.