If the mechanic is an employee of a 121, 135, or 145, he will fall under a FAA approved training program which should include both initial and recurrent training. The FAA will inspect training records as part of their normal surveillance.
If he is an employee of a good Part 91 corporate flight department that has any sort of standards, he will also receive a decent level of training both initial and recurrent. No sane owner of a multi million dollar plane that they fly on wants untrained people working on their plane.
The mechanics that might not get very good training are the ones employed by smaller non certificated shops or the solo mechanics working out of a t-hangar or the back of a truck. Still even they have to remain somewhat actively engaged in their profession by exercising the privileges of their certificate for at least 6 months out of the previous 24.
Also recall that a mechanic “may not supervise the maintenance, preventive maintenance, or alteration of, or approve and return to service, any aircraft or appliance, or part thereof, for which he is rated unless he has satisfactorily performed the work concerned at an earlier date. If he has not so performed that work at an earlier date, he may show his ability to do it by performing it to the satisfaction of the Administrator or under the direct supervision of a certificated and appropriately rated mechanic, or a certificated repairman, who has had previous experience in the specific operation concerned” per 65.81. This in a way becomes a de facto OJT standard. Of course compliance with this is mostly on the honor system and about the only way that a violation of this part will be noted is if there is an incident/accident or if someone makes a hotline complaint.
That’s my view of it in a nutshell but I could go on and on about it but the above should suffice.