As a performer only, chances are you will not need a license, but every county and municipality is different, so check with your local city and county departments of commerce (if you live in an unincorporated area, then you need only to check with the county). If you are running a magic shop out of your home, that's a whole different game and chances are very good you'll need a business license. Again, that's your city and/or county's jurisdiction.
The California State Board of Equalization administers resale licenses and collects sales taxes. Services are generally not taxable, only those things that are tangible can be taxed. For example, when I owned my golf club repair and customizing business, I did not have to charge sales tax on any work that did not result in me adding anything to the existing equipment. But if I added a shaft or grip, those are taxable, so I collected the sales tax from the customer and sent it to the SBE (quarterly). That's how it works in California anyway. That's why mechanics charge for labor and parts separately: parts are taxed, labor (service) is not. If they did not itemize the two, the whole amount would be taxable. If, as a magician, you sell anything other than your service (for example, you sell Svengali decks after your show), you'll have to have a resale license from the SBE. If you travel, you'll need to become familiar with the sales taxes in any counties where you work. This is because each one is different (higher than the State minimum, whatever that is these days: it was 7.25% when I was in business, but Orange County was 7.5% so that's what I had to charge). You have to pay the sales tax rate in the county in which the transaction takes place. It doesnt matter where you live or where your "headquarters" is. It's where the item changed hands.
Obviously a home-based magic shop will need a resale license. If you are doing mail order out of state, the SBE will help you there in regard to what the current laws are (there used to be states that had reciprocal agreements with California for collecting sales taxes--I never got into that game however).
The resale license is what allows you to purchase things at wholesale prices without paying a sales tax to your supplier (who will require a copy of your resale license, or at the very least your number--all my suppliers required a copy on site) as long as you intend to sell the item(s) to an "end user" who will pay the appropriate sales tax which you in turn send to the State. If you do not sell the item, and use it yourself, you are liable for the sales tax because you are the end user. Get it? Somebody has got to pay! Now, with all that being said, go to your local SBE office and check with them! Tell them exactly what you intend to do. I always found the SBE to be the most helpful of all the government organizations I had to deal with. And besides, as my Daddy always said, "Talk is cheap!"