Contribution room accumulates automatically as soon as you turn 18 and are a resident of Canada, regardless of when you end up actually opening one. TFSAs were introduced by the Canadian government in 2009, so if you turned 18 before 2009, your contribution room would have begun accumulating then instead. Here's an example.
Say you were born in 1993, and are 24 now - this means you would have turned 18 in 2011. To calculate your contribution room, you add up the annual contribution room specified by the government from 2011 to up until and including the current year. The sum gives you the total contribution room you have.