So first of all, you have to research the website of the union you're interested in. If it's "hair and makeup" or "production design" and you don't know how to find them, check with IATSE.
Once you know what union you want to join, check their website to see if they have the instructions for joining. If not, call the union and ask to be connected to the person who can give you new member information.
Deciding whether it's the right time for you to join the union is a whole other topic, one I covered early on, so check the archives.
For more tips and articles by top entertainment industry career coach, the Greenlight Coach, visit www.TheGreenlightCoachBlog.com