Riyadh is a long way from anywhere, so odds are fairly high you'll be arriving by plane.
By bus
The Central Bus Terminal tel. +966-1-2647858 is inconveniently located in the Aziziyah district some 17 km south of the city center; expect to pay at least SR30 for a taxi to get there. Buses from Dammam take a tolerable 4.5 hours, while it's a punishing 10-12 hour haul to Jeddah or Mecca with several stops on the way.
By train
Riyadh's train station is approximately in the middle of the city, with four trains daily to Dammam via Al-Hofuf and Al-Hasa. Try to show up 30 minutes early, as you'll need to pass through security before boarding.
By car
The main East-West road through Riyadh is Highway 40 from Dammam and the causeway from Bahrain to Khobar with other road links mainly leading to the North of the Kingdom.
Most roads are tarmacked, albeit to varying levels of repair. Driving standards are slightly more sensible than those of the city centres, but caution is still needed. Some highways see heavy usage from lorries and petrol tankers, often in convoy.