To tame a wyvern you must steal an egg first. Then you must raise the egg with all the elements it needs like temperature. Once it hatches you have to knock out another wyvern and get milk from it to feed the one you are raising.
I got a level 150 lightning egg and I was so excited to hatch the egg...that when I went to put the egg down I accidentally ate it instead. :( ps4 users: R2 ISN'T GONNA DROP THE EGG YOU'RE GONNA EAT IT LIKE ANY OTHER EGG. REMEMBER THIS. LOGIC BEFORE EXCITMENT.