In order to prepare the peyote for consumption, it should be cut above the root. Make sure not to damage the root itself.
The root will then grow 1-2 new buttons. These buttons can be used fresh or dried.
Traditionally, buttons had been chewed and swallowed. But you can also make a tea out of them, similar to the San Pedro tea recipe. Just pulverize/crush the cacti and put them in boiling water, add some ascorbic acid or lemon juice. After 3-4 hours, filter out the plant material.
You can keep the tea on the hot plate, until most of the water is vaporized. That way, you will be able to drink it faster or you can also add some sugar if you want to sweeten up the taste.