This is an issue that is generally governed on a city level. Therefore, you would need to inquire at the city hall of the city in which you plan to petition. The processes from one place to another will vary greatly, but the internet should be a great resource. Most all municipalities have comprehensive websites to answer such questions.
Start by coming up with a solid business plan. Once you have a good business plan find an effective way to market your plan. A great way to do this is to go door-to-door into the area and explain your plans to the people in the area.
First, set up a business plan. How will you handle customers? How many customers will you have? You need to know the potential traffic, both pedestrian and drive by, that your business will generate. If the business will generate a lot of traffic, the petition will likely be denied. If it is work at home with few visitors, you're good.
The rules for this vary tremendously from place to place; different neighborhoods within the same city can have different rules, for example. First, find out the exact rules from your local planning office. Then, discuss your plan with the neighbors.