Check to make sure the hole is aligned with the button.
Have your child pinch the button between their thumb and index finger (thumb on back of button, tip of index finger on front).
With their hand, have the child grasp the edge of the placket, next to the buttonhole, and gently pull it away from them.
This will cause the hole to open slightly, making it easier to insert the button. Inserting a bit of thumb into the buttonhole can also help.
Encourage your child to push one edge of the button through the hole and grab it with the thumb and index finger. This is the trickiest part and will require practice and coordination.
Once your child gets a grip on the button have them pull it all way through the hole.