"Declaring Supplemental Income:
If you have earnings in addition to you main employment, you must also pay tax on that income. You also have to pay social security contributions on these subsidiary earnings. Basically, any wage or salary is subject to AHV / IV / EO deductions. There is one exception: If you do not earn more than CHF 2,300 in one year with one employer, you only have to pay social security contributions if you choose to.
If you correctly declare your subsidiary earnings in your tax return, you can make deductions for business expenses as you can with your main source of income. If your subsidiary earnings are from self-employment, you can claim the actual business expenses for this activity." https://www.ch.ch/en/declaring-supplementary-income/
You might also wish to read several topics on the ch.ch "Becoming Self-Employed" list:
a. "Commercial Register": No need to register your business in commercial register.
b. "Value added tax (VAT)": No need to file a VAT return since revenue less than CHF 100,000. https://www.ch.ch/en/becoming-self-employed/
So, send an invoice with your name on it. Since you will not have a VAT number, no VAT should be charged to your customer. Declare supplemental income for income tax, after deducting actual expenses, and for AHV (social security) purposes.