Stewards are not really the folks that file the grievances. They are more for acting as a witness and record keeping. With that being said it might be good to get help writing them up the first few times because, at least in my area, the company will single out and even claim some spectre of unprofessional conduct or poor communication on poorly written grievances. It's just the game: they expect a higher chance of success getting these ones thrown out first before tackling ones that are more straightforward.
In most areas I would suspect the most formal way of filing a grievance is in person or over the fax machine.