There is no standard practice regarding the inclusion of tips or service charges on the bill.  Most "local" restaurants do not include a tip of charge, while a number of tourist-oriented venues will.  Visitors should check the bill before adding an additional tip.

The standard amount, when service is satisfactory, is 10% (usually rounded up to the nearest 100 HUF [Hungarian Forint, merely called "forint" when speaking], or 500HUF for a large group). If a gratuity is not left, this indicates to the staff that service was totally unacceptable. Exceptional service warrants between 15 and 20%.

The bill and the tip should be presented directly to the server.  You should not leave payment for your meal on the table, nor should you leave a tip separately after paying the check. The Hungarian practice is to complete all transactions face-to-face and it is wise to follow this, both for the sake of being polite and to ensure all parties are aware the bill has been calculated and paid accurately.

Calculate the bill plus tip.  If you have exact change, give this amount directly to your server, all at once.  Otherwise, hand your payment to the server and request change so that the server walks away with the check plus tip during this single transaction.

For example: If your bill was 2000 HUF, the standard tip is 200 HUF.  If you have exact change, hand this to the server.  Otherwise, give the server 3000 HUF and ask for 800 HUF back. 

Remember: Tipping is always at your discretion. Do not feel pressured into tipping if staff or managers challenge the amount you leave and the service was surly or poor, even if the service charge was included on the bill. While wages in this region are considerably lower than other areas of Europe, you should only pay for what you get.