The ZIN membership will be explained in more detail at the instructor training, but it is something I would recommend. It provides a lot of online resources you can use for any questions you might have after going through the instructor training. As a ZIN member, you are given the opportunity to take additional instructor training classes for Aqua Zumba, Zumbatomic, etc. That is a definite plus!
I also received my Primary Aerobic Certification (Group Fitness Instructor) through AAAI in order to build up my resume and learn more about group fitness classes.
Go to Zumba.com and find an instructor training for Zumba Basic 1 near you that fits into your schedule. The training is a full day of instruction and in the end you receive a certificate along with DVDs, CDS, and a manual that goes over all the information you acquired throughout the day. If you are looking to work in a gym or health club you will also want to have some sort of group exercise certification as well.