Most travel agencies could arrange for a bus ticket for you from Luang Prabang, Laos to Chiang Rai or Chiang Mai, Thailand although I would recommend that you just buy your tickets as you go along so you could save some money.
Express bus tickets cost 180,000 to 200,000 depending on which travel agency you ask but if you book it directly to the bus station, it would only cost you 145,000 Kip. Just rent a bike and go to the Northern Bus station to purchase your ticket ahead of time or you could just go there directly on the day of your departure (there’s a lot of empty seats on low season). The trip takes around 12-15 hours depending on weather conditions and the speed of driving (our bus left LP at around 7PM and arrived at Huay Xai around 8AM ).
From Huay Xai bus station, you have to take another songthaew going to the border and it will cost you 30,000 Kip. I found out that it’s the same price even for the locals.
As soon as you arrive in the border you could go directly to the immigration office near the river to get the exit stamp and from there you have to pay for the boat fee which is 10,000 Kip. They also charge an extra 3000 Kip for your huge backpack.
As soon as you arrive in Chiang Khong (the Thai side of the river), you can get your entry stamp and proceed to the waiting tuktuks (30 Baht) that would take you to the local bus station.
The local bus to Chiang Rai from Chiang Khong cost us 65 Baht per person.
Alternatively you could get on a minivan instead which will cost you around 300 Baht (if you buy it from Huay Xai) and 250 Baht if you buy it in Chiang Khong.