If you are a permanent resident of the United States, you do not need a visa to visit Canada. If you plan to work or study in Canada, however, you will need to go through the visa application process.
You do not need a visitor or tourist visa for Canada if you are a permanent resident. You will need to have all of your paperwork up to date and in order, however. When you arrive at the Canadian border, be prepared to prove that you are a permanent resident of the United States (bring your U.S. permanent resident card and your passport).
If you would like to study in Canada, you must go through the general student visa application process. You are required to fill out an application (you can do this online through the Citizenship and Immigration Canada website) and submit an acceptance letter from a Canadian education institution, passport, two recent passport photos, proof of permanent residency in the United States and proof of ability to finance your studies.
If you plan to work temporarily in Canada, you may or may not need to apply for a work permit. The Citizenship and Immigration Canada website has a list of professions that do not require work permits (including athletes, performing artists, public speakers, conference organizers, reporters and emergency workers). Likewise, live-in caregivers, information technology professionals and businesspeople are in special categories with separate requirements. If you do not fall into any of the categories listed, you must have a job offer from a Canadian employer and written permission for the employer to employ a foreign worker from Human Resources and Skills Development Canada. Submit those documents, an application form, a police background check, evidence of financial stability and a doctor's report to a Canadian visa office. You will most likely have an interview with a visa officer in which you will be asked to prove that you will leave Canada when the temporary work visa ends.