You shouldn't need to do this under normal circumstances with Drupal, but for those other times... Just be sure to include class="zebraTable" in the opening <table> tag for any of the tables you want styled, and make sure you have an even and odd class defined in your CSS file. You might also want to change the class names to something other than odd and even to avoid conflicts with your existing styles.
A little doodle from my sketchbook and a quote from one of my all-time favorite authors, Terry Pratchett.
Something tells me that this isn't performing as well as hoped. Just a hunch.
Now I know the more observant among you are saying, "Hey, wait a minute. What are you doing in a Mormon church?" Family reunion. It was outside, but hey, I figure if you're gonna poop, a church seems like about as good a place as any. I call it "returning the favor".