How would I do it?
Actually, I, myself, wouldn't.
Even though I still have the book I purchased on "Chair Caning", .... my RA has rendered my fingers barely able to "hunt & peck" on this keyboard so aligning, pulling n' tugging on caning is out of the question.
If you do it, since you said you glued it already, I suggest washing it using Murphy’s Oil Soap and then apply a liberal coating of the “
clear” Old English Furniture Polish, wiping/rubbing the excess off after 5 min or so, and order one of those
pressed fiber “seat bottoms” and “tack it” down in the spaces between the caning “holes”. That way if you ever decide to “cane it” the caning will cover the holes made by the tacks.