You can stay for up to six months as a tourist, although you're not allowed to legally take any sort of paid job. You can certainly look for one, though. 

Before you move to Canada, you need to figure which immigration program most suits you. Choosing the most advantageous classification is important! Determine your eligibility on the Citizenship & Immigration Canada website,

You must first classify yourself and your job prospects.  Are you:
• Starting a business
• A Refugee
• A caregiver to another emigrant
• Provincial Nominee
• Skilled worker and/or professional
• Skilled worker and / or Professional (destined for Quebec province)
• Enrolled in Canadian Federal Skilled Trades Programme
• Self-employed

You can take a points-based test to determine your eligibility; points are granted based on your educational experience, literacy, job field, language ability, age, and adaptability. The minimum number of points needed to qualify for immigration is currently 67.

Note if you are headed to Quebec, you'll also have some extra paperwork and hurdles.  Check the Quebec Immigration website for the latest. 

Perhaps the easiest method of moving north is to take a position with a Canadian company which will normally sponsor you and fill out the necessary paperwork. Basically, they have to vouch that there no other Canadian citizen who is as well-qualified to take the open position as you. 

Once you immigrate to Canada, you will be given permanent residency (PR) status, which enables you to apply for Canadian social benefits (but does not make you a citizen). You need to renew your PR card every five years, unless you choose to become a Canadian Citizen, which you may do after four years. 
 

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