Where do I have to enter my clients’ information (name, address, VAT No., etc.) in order to see it in my invoices/quotes?

All this data about a client should be entered in the client creation popup or in the popup that opens after clicking on Edit in the Overview panel of an existing client.

You will also find there an 'Other details' field where you can enter all the other information that you wish to display in your documents concerning your client.
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You should enter this information in the Details field under each client (under People > Clients).
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