There is a public sailing club right on Lakeshore road called Venture Sailing club. It is associated with Pointe Claire, so it should be less expensive than joining a yacht club at this point.
Their website is: http://venture-sailing.org/
Not aware of any other places other than the private clubs. I am sure there are a few out there though.
You didn't mention what type of skills you would like to acquire, if you want very good practical courses, that ranges from learning to sail to 3 weeks stages, you can check out: Formation