Use of the VWP for entry to the U.S., however, comes with some strict conditions. You are, at this point, very limited in your immigration options. In particular, you are not allowed to change status within the United States. And a change of status is pretty much the only procedural method for getting M-1 vocational student status while already in the United States.
If you had arrived on an actual nonimmigrant visa (assuming you had not overstayed your permitted time in the U.S.), you might have been able to apply for the change of status using USCIS Form I-539. (Though if you had entered on a B visa for visitors, you would have had to indicate in advance that you’d be looking at schools, and gotten a “prospective student” notation in your visa in order to succesfully apply for a change of status.)
In any case, the change of status option is completely closed to people who entered the U.S. on the VWP.
Your remaining options? The best one is to back to your home country and apply for an M-1 visa through the U.S. consulate there. Don’t even try to go to Mexico to get the M-1 visa: U.S. consulates there won’t accept applications from third-country nationals who entered the U.S. on the VWP.
The U.S. consulate in Canada has no such blanket policy, but is very reluctant to process visa applications from non-Canadians, and may give your application a hard look even if it agrees to review it.