Airline loyalty systems are multifaceted in their benefits, and which program to choose varies a great deal depending on what kinds of rewards you prefer, which airline you take, which fares you purchase, and which routes you fly. However, frequent flyer programs are designed to get you to spend more money with a particular airline by providing extra benefits and services that make it worth it (or at least make it seem worth it). It is not really a path to discounted travel per se.
I don't want to discourage you from learning about frequent flyer programs, or taking advantage of the program offered by whichever airline(s) you will fly. It is true that you can use miles, for example, to take more and more expensive flights than you would have otherwise. The theory is you fly cheap (or paid-for) tickets, then redeem the miles for a premium cabin on some world-class airline you would never or could never buy a ticket for.
For a more mundane example, consider baggage fees. As an elite frequent flyer, you will probably get an increased allowance and/or have some fees waived, which contributes to your "cheap flights." It might be hundreds of dollars a year if you fly a lot and check a lot of bags. For another example, consider that there are no regular nonstops between YVR and GVA, meaning you will need to connect at least once somewhere along the way— London, Montreal, Paris, somewhere. Every connection carries an additional risk of delay or cancellation. The airline will give an elite frequent flyer priority for rebooking in the event you miss your connecting flight, so you could potentially save many hours and many dollars on hotel rooms and taxis while stuck at a connection.
But you'd need to accrue 25,000 or 50,000 qualifying miles in a program year to do it, and that may mean choosing your "home" airline even when a competitor might be cheaper or more convenient, or in extreme cases, doing a mileage run to ensure you maintain that status. At some point, it's not worth it any more. When I used to fly United a lot, I was willing to pay a not-insignificant premium (sometimes over 10%, though not on every flight) out of pocket because as a Premier Executive or whatever, they would offer me express lines, Economy Plus seating, lounge access, seat blocking, upgrade certificates, bonus miles, priority standby, higher meal preference, dedicated phone agents, additional baggage allowance, and similar small benefits that didn't cost the airline much but improved my travel experience greatly. But many of these things are now obviated (e.g. no more upgrade certs), abolished (e.g. no more seat blocking), or diluted (e.g. United credit card holders board with Zone 2). I endured for a while, but revenue requirements were the coup de grace for me.
I started to write out all the variables to consider, but I fear that it would just make this already-lengthy answer more confusing and the selection process more daunting.
So instead, I will direct you to How To Choose A Frequent Flyer Program on the BoardingArea blog, the Frequent Flyer Basics page at FlyerGuide, and the FAQ Which Frequent Flyer Program to Join? Help Is Here! thread at FlyerTalk.