Now that you have your strategy, start with the highest interest rate card and call them first. Tell them that you think your interest rate is too high and that you would like them to lower it. If they hesitate, mention that you have a lower interest rate card (tell them the interest rate on it) and that you are considering transferring your balance to that other card if they can't lower your interest rate.
This method will work the majority of the time. However, it has better success if you are always polite, don't yell, and don't get mad. If they do not offer to lower the interest rate the first time you call, call back a couple days later to see if you get the same response. If you're interested in reading more, check out: Tips to Reduce Credit Card Debt.