I can not take claim to all of the info and ideas below, much of my method is from my own research online, with a bit of my own twist added.
Supplies:
Viable mature Psychotria viridis leaves
Large glass jar (mine used to hold pickles)
Small enough pot that will fit into the jar (I'm actually using plastic solo cups, be sure to make holes for drainage)
Pine bark based soil or Sphagnum moss or perlite (no peat based soil), there are several other options for soil
Rooting hormone such as Indole-3-butyric acid (strictly optional, roots will still form without it)
African violet fertilizer (optional as well)
Before we begin, let me say that this plant is a SLOW GROWER, so please have patience.
There are several different methods for planting the leaves to prepare them to propagate, I've heard of people burying them at a 45° angle with most of the leaf protruding, or there is the 'accordion' method, where you break the main stem in several places, and then partially bury the result. There are also stories I've read where they would actually break the leaf into pieces, and then bury each of them separately, and still getting positive results. Personally I've chosen to use both burying at a 45°, and to use the accordion method. Next you will want to water the soil until the water runs out of the drainage holes. Since I chose to use fertilizer, I diluted it into the water before watering the leaves (as per the label's directions).
So now that you've got your leaves planted in the method of your choosing, the idea now is to use the glass jar as a makeshift terrarium; hopefully it's been cleaned out and all labels removed. What I've done is use the lid of the jar as the base for the pot, so the jar is actually sitting upside down with the pot inside siting right side up. At first I was a bit worried about it running out of air after a while, so I've been opening up the jar about one a week to give it fresh air and that seems to be working just fine. You will want to place your newly made terrarium somewhere that it has partial sunlight. Keep in mind, this plant's habitat is under the canopy in a rain forest, so it's used to having less light.
Depending on method chosen, environment, health of the leaves, etc.,
it will be slow. It can take anywhere from 1-3 months before you see any roots forming, and another 1-3 months until you see the new plant start to shoot up. It might even take longer than that!
So whatever you do,
Be Patient, and you should see results
This is after roughly two months of growth... sorry if the quality of the pictures is poor