How do you make okra mucilage?

It depends what you want to use it for. You get it as a byproduct when you boil Okra for eating (it's in the water).

I was looking for a way to use it as a formation aid in papermaking, which allows the fibers to be suspended longer for smoother, more even paper.

According to Papermaking with Garden Plants & Common Weeds by Helen Hiebert (excerpt found through google Books), Tom Bennick puts half a pound of okra fruit into pantyhose (think large tea bag), which he then soaks overnight in a gallon of water. When he removes the fruit, the mucilage in the water (formation aid), is enough for use with one pound (dry weight) of fiber.

BTW - 1) you don't have to include the seeds in the pantyhose since the seeds contain no mucilage., 2) the roots from other mallows can be used, too, in the same measurements, 3) the extraction does not last very long; it needs to be refrigerated and used quickly.

If, however, you want it purified for scientific purposes, and you have access to a lab, then you might find helpful the information in Studies on the Mucilages Extracted from Okra Fruits (Hibiscus esculentus L.) and Baobab Leaves (Adansonia digitata L.) by Woolfe, Chaplin, and Otchere (the pdf is available online).