If the meal is being accompanied by a beverage, never fill your own glass. Your neighbor will fill your glass and you are expected to return the favor. As you finish all your food, feel free to ask for more, this is a compliment to the host. If you're completely done eating (save some room for dessert though), finish all the food on your plate. Often times dessert will be served and many times coffee or tea is offered and expected to be accepted.
If dining out, as the bill comes, the host or inviter should pay for the whole meal. If dining without any locals, summon the waiter or waitress by making eye contact; waving or calling a server over can be considered rude. In regards to tipping at sit down restaurants with a waiter or waitress, round up or tip about 10% of the bill. Small tips to bar tenders are also appreciated, but not necessary.
Drinks
Bosnia & Herzegovina's most popular drinks are essentially Turkish in origin. Turkish coffee is a common wake-up for Bosnians, but is drunk throughout the day. Tea, soft drinks, juices, and milk are also widely available.
Despite being a primarily Muslim country, most Bosnians do drink alcohol or at least accept the fact that people around them drink. Two of the more common local drinks are rakija and sljivovica, which are flavored alcoholic drinks similar to brandy; often times made from plums and grapes. Despite this local specialty, beer is still the most common alcoholic drink, but all popular international beverages are available, including imported beers, wines, and hard liquors.
Generally speaking, the tap water is safe to drink in Bosnia & Herzegovina, but check with locals for any particular regional differences as the Balkan Wars may have contaminated some areas. Also, many people may have troubles adjusting to the local tap water, as it will most certainly be different from what your system is used to.