To add your VAT ID, go to Account Settings > Taxes > VAT Registration.
Your information will be verified by the eVatR, the German VAT number validation service. To validate it, please make sure that all your information in your account matches perfectly the one registered at the European Commission. If you do not remember exactly what information was registered, you can go to the VIES to access it.
The above content is no tax advice. Please clarify with a tax advisor your individual tax obligations.