In summary, the new rules changed tax obligations for:
Imports of goods: all goods are taxed (exemption for goods below EUR 22 was removed)
Sales of goods in the EU: sales within the EU are taxed in the country of consumer
If you are selling goods directly - ie not via a marketplace, you remain responsible for collecting and reporting of VAT on all sales to your customers.
You can use the IOSS or OSS schemes to simplify your obligations for B2C sales or use standard VAT registrations and file VAT returns under these registrations.
More information about how the new rules apply to specific transactions can be found at: https://taxually.com/e-commerce/