By plane
The nearest airport on the Thai side is in Udon Thani, 56km away. There are direct shuttle buses four times a day between the airport and the Friendship Bridge 2km outside Nong Khai, plus taxis and minibuses that will take you in to Nong Khai proper.
Thai Airways and Air Asia operate flights between Bangkok Suvarnabhumi and Udon Thani. Nok Air operates a service between Bangkok Don Muang and Udon.
By train
Nong Khai is the terminus of the Northeastern railway line from Bangkok via Khon Kaen and Udon Thani. The trip takes 10-12 hours and a first class sleeper ticket from Bangkok to Nong Khai or vice versa is currently about 1200 baht, and a second class sleeper ticket not bad for the price is 748 baht. Sleepers often sell out at peak times so you may need to book in advance.
Shuttle services now operate onward from Nong Khai to Tha Nalaeng, Laos near Vientiane four times a day, synced to the arrivals and departures of the Bangkok trains. You can only buy tickets at Nong Khai station, and you need to pass through immigration as well. If coming in on train #69 from Bangkok, there's a 90-minute window to do this. Once the formalities are done, the trip itself across the Friendship Bridge only takes 15 minutes. Visa on arrival is now available on the Lao side
By bus
There are departures to Udon Thani at least once per hour from the BKS station on Prajak road. The hour-long ride costs 20 baht in 3rd class non-air con. 40 baht in 2nd class air con.
There are several departures daily from Bangkok ~9 hours, Khon Kaen 110 baht, class 2, with stoppage at Udon Thaniand across the border direct from Vientiane 55 baht, 17000 kip, two hours via the Friendship Bridge.
A 1st class bus service connects Nong Khai directly with Suvarnabhumi Airport the new BKK.