Do I just open the canopy and jump out? Is my parachute always strapped to my back during flights or do I have to put it on?
Yes, you would have received instructions. They would be committed to memory and if you valued your life, you would be sure to memorize them well. On the other hand, there wasn't much to memorize. The procedure was relatively simple, as any reasonable life-saving procedure.
So, your cockpit is not on fire, you have a few seconds to spare, you can act methodically instead of frantically.
First of all, jettison the canopy. Don't just open it, because due to some odd factors it might close back again. We have time to spare, but no time to lose. You also need to unbuckle your seat-belts and don't forget to detach your radio cable and oxygen supply. If you forget, it might prevent you from leaving the aircraft. Again, no time to lose. Now, do you have aileron authority? You do? Great, perform a half barrel roll. Now you will simply fall out of the cockpit, also minimizing the risk of hitting the vertical or horizontal stabilizer (though the risk will always be there, this is exactly what killed Hans Joachim Marseille, in my opinion the best fighter pilot of WW2).
If you cannot roll the plane on its back, you have to climb out of the cockpit onto the wing and just jump. Be careful as the air striking your body will try to force you back into the cockpit. If one wing is angled downward, you can attempt to slide down on it just a little bit to avoid the stabilizers.
Now, you're in the air. When do you open the chute? It depends. You might want to do it immediately, but not necessarily. Say we're in the Battle of Britain. If you're an Allied pilot and there are Luftwaffe planes near, wait as long as you can since they might attempt to shoot you out of the sky. Also, if you're near the Channel and the wind is blowing towards it, wait as long as you can so as not to be blown over the water. And if you're falling from very high up, you might want to wait a bit so as not to die of boredom during the long descent.
And yes, you would always have your parachute strapped to your body, though not necessarily to your back. Some would be touching your buttocks in such a way that when you sat in the cockpit the parachute bag would be a cushion upon which you sat. The benefit of seat-type chutes was that their harnesses restricted your movement considerably less.
This is a generic procedure, which would vary from aircraft to aircraft. For example, the P-39 Airacobra has no canopy thay you could jettison, just a door. ^Second^aviation^question^today.^Lovin'^it.
[EDIT: typos]
Many aircraft manuals from the era (and up thru the present) include bailout procedures. There are several scanned and transcribed handbooks online with details. Here is one for the P-51 Mustang. P. 24 details the emergency canopy release location, Emergency Procedures are enumerated beginning on p. 80, and bailout procedure is p. 87. A critical step is ejecting the canopy, and the subsequent procedure focuses on not colliding with the aircraft post-jump.
Fighter pilots would almost always fly strapped into their parachutes for the whole flight. There is no room to store a parachute, much less put one on, in the cockpit of your average WWII fighter. Some bomber crew members would be unable to wear parachutes in the more cramped spaces: theirs were stored in an accessible area and donned before bailing out.
One interesting aspect of bailing out was intelligence related. Several airmen who bailed out over occupied territory were repatriated by various resistance groups. In this case, a decision may be made to transfer the airman to a different theater of the war or to a non-combat role due to their accrued knowledge of resistance networks, which would be a major liability if they were shot down again and captured.
Follow-up question: if a pilot was shot down deep inside enemy territory (for example a British pilot bails out over the heart of Germany), how common was it for them to attempt/succeed in escaping to friendly territory? It seems that before the days of GPS and rescue helicopters the chances of making it out of the country would be virtually nil.
As per the other comments, you'd be sitting on or in your parachute, and would certainly have had instructions. Exact procedure would depend on the aircraft you were flying and situation you found yourself in; there are a couple of first hand accounts of baling out in "Ten Fighter Boys", written by pilots of 66 Squadron under noms de plume and first published in 1942:
"Duggie": "When I was about 2,000 feet, and with the airspeed at 180 m.p.h., I started to abandon aircraft in the manner so often discussed and recommended in the pilots' room. The idea was to turn the aircraft on its back, then drop out, pulling the "ring" at one's own convenience. The thing which hadn't been stressed, but which proved the most important, was that the "harness" should remain fastened until the last moment, when, on extracting the release-pin, gravity (according to the venerable Mr. Newton) should assist exit."
"Bob": "Flames from the oil tank were bouncing about in the corner of the cockpit, and spurred me to greater efforts. Off came the Sutton harness release ring; I stood up. Blast! I'd forgotten my helmet, and was still fastened to the aircraft - ducking back out of the slipstream I actually tore the helmet leather as I wrenched it off. Into the slipstream, again leaning slightly to the left, and hey presto, the wind had plucked me out"