You’ll find buses to Bangkok plus Chiang Rai and Chiang Mai, from where you can link up with routes to just about anywhere else you want in Thailand.
Unfortunately though there is no transport to either Chiang Saen or Phu Chee Fah. If you’re feeling adventurous (and lucky), you can in theory reach either with some songthaew-hopping though locals point out it is easier to actually go all the way back to Chiang Rai bus station and change. Odd, but these are, at the end of the day, small towns.
Battered old red buses depart from the permanent market taking two hours to reach Chiang Rai and charging 65 baht. This is the direct route passing by Phayamengrai and they leave every hour on the 30 minute mark from 04:30 to 15:30.
For Chiang Mai, also in theory stopping at Chiang Rai (though do check) are the following services by Green Bus:
07:15 arriving 13:00 – 279 baht
09:45 arriving 15:30 – 279 baht
09:45 VIP arriving 15:30 – 434 baht
10:30 arriving 17:30 – 284 baht
They also run Bangkok buses for 655 or 764 (VIP) both departing at 15:15 and scheduled to arrive at 05:00. Government-run 999 and privately owned Sombat Tour also run Bangkok buses with the former being cheaper and the latter, with limited seat number VIP buses, more expensive. There’s no central bus station and each company’s buses leave from outside their respective offices. Green Company is on the left just after the bridge whilst 999 and Sombat’s are on the right hand side slightly further up.
Slow boats for Luang Prabang via Pak Beng depart Huay Xai daily around 11:00. Many travellers purchase these tickets beforehand as part of packages obtained in Chiang Rai, Pai or Chiang Mai for example but any guesthouse in Chiang Khong will sell you one too. However if you’ve got this far without one you may as well save some money and buy it once across the river in Laos. In Huay Xai slow boat tickets go for 950 baht while in Chiang Khong you’ll pay between 1,250 and 1,650 baht for the same ticket. Indeed some guesthouses will also offer to book accommodation in Pak Beng for you. In high season it’s a good idea to book this overnight stop in advance but you can of course reserve from Huay Xai too.
A private tuk tuk to the bridge and immigration will set you back 150 baht although there are also regular shuttle songthaews running back and forth for 50 baht. You can flag these down anywhere along the main street and they arrive and depart from just in front of Thai immigration at the bridge.