One notice upfront: The following only applies to visitors, not to persons with a permanent or secondary residence in Austria or within the EU.

All visitors not resident in the EU are entitled to a refund of Austrian value-added tax, which is included in the price. Minimum purchase: EUR 75.01. This Is How It Works:

There are two major organizations in Austria that are responsible for refunding for Value Added Tax – Global Blue and Tax Free Worldwide. Depending on which organization you choose, ask the salesperson for a filled-in Global Blue or Tax Free Cheque (name and address abroad have to be filled in) and for the appropriate refund envelope with a list of all locations where cash is refunded. The original bill must be attached to the Refund Cheque.
Upon leaving the European Union, you show your purchased items to the customs officer and get the appropriate customs stamp. Without this stamp a refund is impossible. You can receive this refund at one of more than 700 refund locations worldwide, for example at airports or in your home country (check on the Refund Envelope), or you can mail your Refund Cheque to Global Refund or Austria Refund and request a transfer.
At the Vienna Airport, you can find the refund locations of Global Blue and Tax Free Worldwide in the shopping area or at Pier Ost (A Gates) in the immediate vicinity of the customs booth or at the baggage claim.
The average refund after deduction of handling charges is about 13% of the original price.