As stated above, you typically have three ways:
Marriage / Common-law (spousal sponsorship) - takes a while
Common-law is when you are living with your partner for 1 year, and you need proof of this to go any further (bills in her name, her name on a lease)
Work permit - difficult
She needs to be accepted by a company or work program within Canada
Study permit - expensive
She needs to be accepted to a university within Canada before applying for the study visa. She (or someone) would be paying expensive international study fees (usually 2.6 or 3 times the normal tuition rate).
There are loop-holes however, somewhat. Expensive ones, considering travel. I am from the UK myself and now living in Canada with my Canadian fiance. We met each other online years ago and I finally decided to take a trip over here, I'd always wanted to see this country and I thought I'd visit this person I knew - two birds one stone. It was a last minute decision but I decided to stay over here after much deliberation. We fell in love, he agreed to help support me until I could get back onto my feet over here with work or study, whichever came first. We did it/are doing it like this:
I came over on a standard visitor visa. So from the UK we can stay in Canada for up to 6 months, but cannot work. We can, however, study academic programs that take less than 6 months without needing any extra visa. We can drive on our UK driving license for 3 months only though (no idea why). After 6 months we must go home and stay there for 2 weeks before we are allowed back to Canada. Ofc I couldn't dilly-dally around like this forever, so I decided to carry on with my studies and take up another degree. I applied to a university, went home to England for Christmas and by the time I got back to Canada I was accepted. Be aware, when you enter Canada without any return plans (in honest hope with honest plans to stay there legally, with no illegal actions) they are still very strict. If you do not have a return ticket they will take you back to their offices at the airport and ask you everything about yourself. Why you are coming, why haven't you got a return, where are you staying, who are you staying with, what do you do, what did you study, what are you planning to do in Canada, why, how are you able to afford it. They will search your bags again. But as long as you are sincere and have a definite plan, they are usually nice enough. This is what happened to me, and the immigration officer understood my plans to study and live with my fiance, so gave me an updated visitor visa that gave me a number to my name so I could apply for visa's and more from within the country (usually you need to apply for study/work permits outside of Canada). With this I could then apply for a provincial driving license so I can drive after 3 months, and I could also apply to change my visa status from visitor to study/work without having to leave the country. Within a few weeks I was approved for my study permit. Our wedding is this fall. At that time, we will apply for spousal sponsorship and update my visa once again to permanent resident. This process usually takes around 6 months on marriage sponsorship (can be longer, can be shorter). PR status means you'll have the full rights of a person born in Canada, besides a few - cannot vote, cannot join the armed forces etc. Once PR status is gained through marriage you have 2 years of "probation" to prove your relationship is legitimate and strong. You are then able to apply for citizenship. Which is a whole other goose-chase.
If you truly want to stick with this person, you both need to be vigilant. It's a long, expensive and sometimes irritating process. But stick to your guns, be patient and smart and you'll get there.
