California does not license private tutors. However, if your prospective employees are to work with young children, and you want to avoid potential liability, then you will probably want to obtain a fairly substantial background security check to ensure that the employee has no record of sex offenses or other potential risks (drug use, alcoholism, etc.).
As far as liability insurance goes, that's a project for an insurance agent. The question largely revolves around the size of your business, because the more assets accumulated in the business, the more risk of legal action and the more insurance coverage required.
Other than that, you will need to either incorporate or create a Limited Liability Company to further protect yourself against risk. You will also likely need to set yourself up with a payroll company like ADP, because dealing with payroll taxes (unemployment insurance and workers comp, etc.) can be a major hassle and very difficult to maintain unless you're planning to hire an accountant.
That about covers it. Let me know if you have questions.
Hope this helps.
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