Nong Khai has no airport. The nearest one is at Udon Thani, 55 km to the south, with frequent flights from Bangkok. From Udon Thani, buses and minivans run to Nong Khai in about an hour.
From Bangkok, overnight trains run directly to Nong Khai -- the sleeper is comfortable and arrives in the morning, which is the civilised way to do it. Express buses also make the trip in about ten hours. If you are coming from Vientiane, buses cross the Friendship Bridge regularly throughout the day.