Sacha,
Welcome to Alberta, the Calgary area and fishing! Whether you fly fish or cast with gear, (a spinning type rod with a lure, possibly with a float or weights as well), as my learned friend above says, you are off to a good start by desiring to know the regulations. Frankly, I have seen too many "new Canadians" (I am not saying you are one, I am referring to new residents of Canada) who fish without knowing the rules or, in some ways even more importantly the customs and courtesies or etiquette of fishing. Good for you.
The recommendation from Peter above is wise. A professional guide will start you off very nicely and will likely take you somewhere he/she is nearly 100% sure you will actually catch fish which is a positive reinforcement when starting out. Visit some shops, don't buy anything yet, but browse around and ask questions. Some shops have beginner fishing classes, mostly for fly fishing as it is more challenging and difficult to master.
Talk to friends and colleagues at your place of employment or education. Try and find an experienced fisherperson who is willing to answer questions and maybe take you along for an introductory outing. This website occasionally has people who post their desire to fish with someone from the area. Until you gain enough experience in fishing, finding your way around and water safety I recommend you treat fishing like SCUBA divers treat their activity: going solo is a no-no. Fish with a buddy - keep them in sight at all times.
Another great source of information in addition to the interweb are books. Go to your library, and read as much as you can. The interweb has thousands of videos about just about every possible aspect of fishing I can think of. A great way to while away the non fishing hours of winter.
Finally, within the fishing regulations guide you will find reference to stocked waters. These are places where a portion of your annual license fee are used by the province to place fish in waters where you are allowed to harvest them for food. A lot of these places are easily accessible, quite safe (if crowded at times), and have amenities like close parking, an outdoor toilet, picnic areas and so forth. It is a good place to start and develop your skill level.
I wish you good luck and many happy hours on the water.