If you are a business, you need a license, whether or not your business is in your home. Check the City for license/business requirements. Plus you'll need a gross receipts tax number for your business. You get that from the state.
These are the rules for home occupation in a residential zone:
(g) Home occupation and sign identifying the activity, provided:
1. The activity is clearly incidental and secondary to use of the premises for a dwelling.
2. Only members of the residing family are employed.
3. No stock in trade is manufactured, displayed, or sold on the premises, except a small stock of art objects and custom sewing created by a resident of the dwelling is allowed.
4. All business activities are conducted entirely indoors.
5. No more than 25% of the floor area of the dwelling is devoted to the home occupation. No more than 5% of the floor area of the dwelling is devoted to storing stock in trade.
6. There is no external evidence of the activity, including, but not limited to, the parking of commercial vehicles, inordinate vehicular traffic, outside storage, noise, dust, odors, noxious fumes, or other nuisances emitted from the premises.
7. Health care (including physicians, nursing homes, massage, and the like) shall not be considered a permissive home occupation.
8. One related on-premise sign is permitted, provided:
a. It does not exceed one square foot in area.
b. It is a non-illuminated wall sign.
You will need the tax certificate to apply for the City busines license. They will check the zoning for your address to verify that home occupation is allowed. Depending upon you billings, you will have to file a report with Tax and Revenue monthly, quarterly, or yearly and remit the GRT you collected. If you are teaching one on one the number of students should not be an issue. If you are doing groups, it might become an issue with parking, for example. The sign is allowed but not required.
Good answer, Hunter. I was wondering about this myself recently...