Plenty of airlines fly into Belgrade — JAT Airways and British Airways both fly direct from London — so you shouldn’t have a problem getting there. The big hitch is that as yet, no budget carriers fly to Serbia. Buses and trains run from most neighbouring countries — it’s only 7-8 hours from Zagreb and Budapest by rail.
Serbia’s train network won’t rival Switzerland for speed and efficiency, but does serve some of the bigger towns throughout the country. Buses run pretty much everywhere. Driving yourself is probably best avoided – Serbia’s roads leave a bit to be desired.