Learning a few Slovak words helps break down Slovak reserve, even just “hello”, “goodbye” and “thank you”. If you’ve been travelling eastwards, your Czech will do fine, as all Slovaks understand Czech (an equation which doesn’t work in reverse).
When tipping, Slovaks round up to the nearest euro or two, but as a foreigner it’s courteous to tip ten percent. When you are introduced to strangers, shake hands, and don’t use first names when addressing older people. Casual greetings like ahoj are only for close friends. Wish fellow diners a good meal (dobrú chuť) before starting, and make a toast (na zdravie) before drinking. If you are invited to a Slovak home you must take off your shoes at the door, even when told not to (they’re just being polite), and if you’re invited to eat, bring wine or chocolates.