My first advice would be to consult a planning/zoning attorney in your area. When you're undertaking an appeal, you need to understand the legal basis for the same (that is, it isn't always based on whether you think the zoning administrator got it wrong). There are a lot of nuances to land use law and you want to make sure that you are asserting every legal argument you can possibly assert. If you don't, then you may be foreclosed from pursuing action later down the road.
Whether it's in court or before a planning commission, people who represent themselves are proceeding at their own peril. If this decision impacts you, please do yourself a favor and consult an attorney.
DISCLAIMER: Brandy A. Peeples is licensed to practice law in the State of Maryland. This answer is being provided for informational purposes only and the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship. For legal advice relating to your specific situation, I strongly urge you to consult with an attorney in your area.
The procedures for appealing a zoning decision vary from city to city. You should be able to find out what they are for your area by checking the zoning commission website. If they don't have a clear link, then you will have to look through the ordinances.
If you want to avoid doing all the homework, then you will need to contact a local attorney that handles zoning matters. Check with the city clerk and ask if there are attorneys that appear on matters on a regular basis.
See Ms. Peeples' answer. It is very good.
Any comments offered are not intended as legal advice. This attorney does not know the specifics of the particular case sufficiently to offer legal advice. You should hire a lawyer who can evaluate the details of your specific situation before offering advice.