rdt2449,
The airborne qualified personnel in the Canadian Army are currently concentrated in the "Jump" companies within the Third Battalions of each of the three regular force infantry regiments (The RCR, PPCLI and R 22e R). To get there you first have to successfully complete basic military training, the soldier's qualification and basic infantry training. On enrolment you will be offered a position with one of the Regiments, following these initial courses you will have an opportunity to identify which battalion you would like to serve with, but keep in mind that you will be sent where the Army and the Regiment need you.
Once in the battalion, you will have opportunities to be selected for a variety of courses, first those that will make you more employable as a soldier in your initial rifle company, then possibly other courses such as parachute training. While most slots for the jump course will go to the Third Battalions to support their airborne tasks, I expect there will be chances for soldiers from the other battalions to attend as well. (Someone in the Battalions now can confirm this.)
Positions for the parachute courses will undoubtedly be competitive, and the best way to get there is to be the best at everything you are assigned, while ensuring that your superiors know you want the training. By ensuring they know I am not advising open declaration at every opportunity, I suggest you take care to bring it to the attention of your supervisors when you have interviews that are open to discussing future training desires. For soldiers in the battalions, submitting a memo to your platoon commander once a year requesting specific training is a polite and official means to bring the subject to their attention. After completing the parachute course, you can then request a move to the jump company of your Regiment. Patience and dedication to current reponsibilities are the best approach, proving you deserve it is better than just declaring you want it.
Once you have served for a few years, you can consider JTF-2. That unit has very high standards and is something to be worked toward over time as you better understand your own capabilities and personal expectations.
You'll find the subjects of fitness, infantry training, para and JTF-2 have been dealt with in extraordinary detail on the forum in the past. I suggest you start with the FAQs in the Infantry and Recruiting boards, then use the search engine to find other related material.
The FAQs can be found here:
Infantry -
http://army.ca/forums/threads/17073.0
Recruiting -
http://army.ca/forums/threads/17067.0