Read about it. If you have an interest in Zydeco dance, then its origins will likely interest you as well. Find a book that includes not only the history of the dance, but a description of the steps involved. Online resources are available as well. The website Zydeco.org gives a history not only of the dance, but festivals in Louisiana where you can meet others with a similar interest.
Watch and learn. Why attempt something new in public when you can try it at home first? Feelings of self-consciousness will subside as you watch others "letting the good times roll." You may not personally know anyone who can dance like a genuine Cajun, but an Internet search will lead you to videos of experts showing off their moves, as well as to workshop-type videos for beginners. After a while, you'll get used to moving in that particular Zydeco rhythm.
Listen to the music. Once you have an understanding of the roots of Zydeco and have seen how it's done, invest in the right music. Recordings are available to download or to buy on CD. If you don't happen to have a local Zydeco radio station, it's easy to find one with a quick Internet search. The popularity of Zydeco music and its uplifting, party-time feel make it in demand, and Louisiana is proud to share its music with the world.
Go for it. Now that you have a firm foundation in Zydeco dance, get out there and have a good time. Find one of the Cajun festivals that commonly pop up in most towns. Odds are you'll be surrounded on the dance floor by beginners such as yourself (unless you happen to live in bayou country). You can also search your local newspaper for special dance events in your area.