An ema is a small wooden plaque, mass produced for the shrine that sells it, with a printed or stamped image on the front, commonly the shrine's emblem or the current year's zodiac animal, and it is bought pre-made rather than commissioned individually, the personal element coming entirely from what the buyer writes on the blank reverse side.
Who writes it, and what for
Any visitor may buy and write an ema, there is no restriction on who may do so, and the practice covers everything from exam success and safe childbirth to general good fortune, written in the buyer's own hand and hung on a dedicated rack in the shrine grounds alongside hundreds of others left by strangers.
A planned, collective disposal
Ema are not meant to be taken home or kept indefinitely, they accumulate on the shrine's rack and are collectively gathered and ritually burned by shrine priests, typically at year end or during a specific festival, a purification by fire rather than an informal clearing away of clutter, which is why an ema left at a shrine is understood from the outset to have a fixed, communal, and eventually fiery end.
No restriction on the wish itself
Shrines place no limit on what a visitor may write, a request for exam success sits on the same rack as one for recovery from illness or a safe birth, and the plaques are read by no one in particular before being burned, the writing itself, not any priestly review, is treated as the completed act of prayer.