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As a newly started company in the EU I'm a not 100% sure on how VAT works internationally.
I'm going to double-check with the Swedish authorities to make sure but maybe someone here might have some information.
This is how I understand it:
When I sell to another company at a fair like Essen, I will need to create an invoice for that company. This invoice should include their VAT number, although the invoice does not include VAT in the cost.
Afterwards I will submit a report to my tax offices with the invoices representing sales to another EU country so I don't pay VAT for them myself.
Regarding selling to private customers, I will write a daily report on the amount of sales + money received. This will include VAT.
If anyone has more experience in this please let me know.
You're generally correct, however I would double check if this also applies to on-site sales, or (which I think is at least a faint possibility) that on-site sales must apply local (eg German 19% VAT) taxes.
I have highlighted one part of your post just to stress that your invoice must (not should) include the VAT ID. In our company we always use an online checker to see if the ID is actually valid, because if it's not you'll get a lot of trouble afterwards.
As far as selling to individual customers is concerned, you must include 19% VAT in the end price. This means you cannot add it at the cash register or something similar. The price tag is what the customer pays, incl. VAT.
Note: Books only have a reduced tax of 7% VAT!
Diclaimer: Don't take my word for anything, better check with your authorities.