Welcome to the forum! There are plenty of ways to get a wyrm. You can breed one during a season by contacting the handlers for permission and then submitting a form OR you can snag a convention wyrm. Sometimes there are even wyrms posted online up for grabs but you never quite know when those will show up.
http://twilightdays.org/wyrmwiki/index. ... dler_Guide The Handler's Guide explains this all in MUCH better detail.
And if you DO decide to look into breeding, check out that guide too.
http://twilightdays.org/wyrmwiki/index. ... ding_GuideIt goes through the steps on how to do so.
Hope you have a great time. Feel free to ask more questions!