Berets were first adopted by Canadian tank crewmen before WW II; I believe the first Tank Regiments were raised in either 1921 or 1936 (when the big militia re-orgs took place).
In WW II, the maroon beret was adopted by paratroopers mid way through.
In 1943, the khaki beret was introduced to all other arms and services of the Army, replacing the Field Service Cap (a wedge type cap, or sidecap). Some units weren‘t issued the new beret until 1944 (I think the Royal Montreal Regiment was one example).
The khaki beret remained an issue item to the end of the war. In the post WW II era, coloured berets were worn by different corps; navy blue by artillery, engineers, etc., scarlet by infantry, etc. I‘m not clear on the regs during this time. In the late 1960s, the rifle green beret was introduced as part of the new CF uniform when all three branches of the service were unified. Black was still worn by the armoured corps and maroon by the Airborne Regiment.
Correct way to wear it - see my book DRESSED TO KILL, but in brief, the leather sweatband is level on the head, two fingers above the eyebrows, with the ties tucked in or cut off. The cap badge is directly over the left eye and the excess material pulled over smartly to the right side.
WW II berets were floppier than modern ones, with the excess material drooping down to cover the right ear. Modern ones are neater in appearance.
Stiffener is often used to back the cap badge, and berets are often formed with a "trench" behind the cap badge. Not sure if this is regulation or not these days.