You cannot tame an adult wyvern, you will just waste your time if you try, you need to raise one from an egg.
Firstly go to the Wyvern cavern near the volcano or the Wyvern nests just before you get to the desert zone, and steal an egg from a nest... make sure you are on a fast flyer as Wyverns are not all that found of having their eggs stolen and will attempt to flame, electrocute, freeze or gas you to death for it.
Once you have the egg, you need to incubate it, take it back to your base and stick it between either 4 air conditioning units or about a billion torch stands (Maybe over estimated amount there?) and the incubation will start and eventually a baby Wyvern will appear!
The next step is to trap a Wyvern and get some of it's milk, make sure the wyvern is female.
Once you have the milk, feed it to your baby Wyvern. The baby Wyvern will need care such as going for a walk or a cuddle (it wont bite!)
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