By ship
Ferries cross between Chiang Khong, Thailand and Houay Xai for 40 Baht + 10 Baht for luggage. Immigration offices on both sides of the river close at 6PM. The small ferries carry only a few passengers and leave as soon as there are more than a couple of people on board, so you do not have to hang around. The landing point is near the middle of the town center. In Chiang Khong, the ferry pier is at the northern end of town, a 30 baht tuk-tuk ride from the bus station.
By plane
Houay Xai's tiny airport has service three times a week to/from Vientiane on Tuesdays, Thursdays and Saturdays. Until November 2010 there was one flight a week to Luang Prabang on Saturdays, but none in the other direction. There is talk that this flight will resume.
By bus
The 9:30am bus from Luang Namtha arrives at the bus station 2km out of town at around 2:30pm. Tuk-tuks charge 10,000 kip to the border or guest house of your choice in town.
Upon arriving in Houay Xai, you might be approached by touts asking about your next destination. If you answer Luang Prabang, you will be pressured to reserve a ticket on a VIP bus, because the bus is invariably "sold out". The ticket will be priced at something ridiculous like 210,000-260,000 kip, which includes transport to the bus station. Upon arriving at the bus station, you will be handed a ticket with the actual price, 110,000 kip, staring back at you as a stinging reminder of your gullibility. At the bus station you can get a ticket all the way to Vientiane for 210,000 kip, which should give some indication of how much of a rip-off the touts in town are trying to pull on you.
If you're going to be in Houay Xai for at least a day, simply take a tuk-tuk to the bus station for 10,000 kip and buy your ticket for the day you plan to leave. The extra money you spend on tuk-tuks is more than offset by the 100,000-150,000 you'll save on your bus ticket.