Visas
Citizens of the EU, UK, USA, Canada, Australia, and many other countries can enter Serbia visa-free for up to 90 days with a valid passport. Serbia is not in the Schengen Area or the EU. You must register with the local police within 24 hours of arrival -- hotels do this automatically, but if you are staying in a private home, you need to register yourself at the nearest police station.
Money
The currency is the Serbian Dinar (RSD). Euros are sometimes accepted informally but you will get a poor rate. ATMs are plentiful in cities and accept international cards. Credit cards are widely accepted in Belgrade and larger towns, less so in rural areas. Serbia is very affordable by European standards -- a good restaurant meal costs 8-15 EUR, and a beer is 1.50-2.50 EUR.
Language
Serbian is the official language, written in both Cyrillic and Latin scripts. You will see both everywhere, sometimes on the same sign. In Belgrade and tourist areas, many younger people speak good English. In smaller towns, a few words of Serbian go a long way. Basic phrases: "Hvala" (thank you), "Molim" (please/you're welcome), "Dobar dan" (good day).
Safety
Serbia is a safe country for travelers. Violent crime against tourists is very rare. Standard precautions apply in Belgrade -- watch your belongings in crowded areas and be cautious with unlicensed taxis. Some areas near the Kosovo border can be tense -- check current advisories.
Tipping
Tipping is appreciated but not obligatory. Rounding up the bill or leaving 10% in restaurants is standard practice.