Fizetek, kérem! = "Check, Please!"
One of the glorious holdovers from times past is the ability to sit in any drink or food establishment without concern of being hurried out the door. Unless the doors are closing for the evening, no one will approach you to pay your bill until you signal that you are ready; therefore, you can linger for hours on end.
Don't be surprised if the person who comes to collect your money is not the person who served you. Many places have a designated cashier who will arrive at your table to collect your money. It may be a few minutes before they arrive, so be patient. Smaller restaurants still have this annoying habit of giving you a small piece of paper with a list of numbers and nothing else to associate them with. If you have questions about it, ask to see a menu to match the charges on the list before you pay or ask the cashier to explain it. If there is a mistake, challenge it and it will be corrected.
Always ask if a service charge is already included. It should show somewhere on the bill, but it is worth asking to make sure. If the service is included, you are not expected to tip. If no service charge is included, add 10% to the bill (12-15% for exceptional service in high-priced restaurants only - though note that the waiter very rarely gets a share of the tip). We like to hand the tip directly to our waiter to make sure he receives it. Never leave the tip on the table and walk out.
The cashier will often remain at your table after delivering the bill, waiting patiently for payment. State the full amount you are paying (bill plus tip), and the waiter will make change on the spot. If the restaurant accepts credit cards and you are using one, then the cashier will bring a portable card reader to your table to swipe the card. If you want to add the tip to the charged amount, you need to say so before the charge is processed; it can't be added to the bill later.
When you really appreciate your waiter, slip some money to him or her privately to make sure the server receives some compensation. During tough economic times, it happens often that when paying by credit card, "suddenly" the credit card machine has died and you will be asked for cash. If you insist that you have no cash and refuse to run to the local bank machine, mysteriously, their credit card machine resurrects from the dead and can handle the transaction. This is usually to aid the establishments'cash flow and avoid paying taxes. Don't be part of their scheme if you really want to use plastic.
It is rare the restaurant that will give separate bills to one table. If you ask, they will often say they can until it comes time to pay, then suddenly they can't do it any longer. If you are sharing a bill, you may want to keep note of your charges to make things easier when it comes time to split the bill.