If you are solo taming one the best thing to do is to get an argent at 200% speed to out run wyverns (220% speed for alphas). The fly into the trench and look for eggs. When you've found one aggro all near by wyverns and fly into the mountains. Since you don't have an egg yet they won't follow you forever, they will actually get distracted by other creatures. After you've lost all the wyverns fly back and get the egg. To incubate either surround the egg with torches or fireplaces. A cheap way to get milk is to lead a low level female wyverns to the manticore arena and get it stuck on one of the buildings. Then just tranq it.
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.