Visa-on-arrival is available at Luang Prabang airport and the price is variable based upon your nationality. You need a passport picture to obtain a visa. If you don't have one, they'll scan your picture from your passport and charge you an additional $1.
You can enter from China overland. Visa available at the border (Chinese citizens need to arrange a visa before. Possible at the Lao consulate in Jinghong. Same day visa available). There are buses from Jinghong to Luang Namtha, approximately 70yuan, taking ~7h.
Buses from the northern bus station travel in Vientiane travel along the Mekong River to Sanakhan (the Lao town opposite Thailand's Chiang Khan), then through the mountains to Pak Lai. From Pak Lai, buses travel south to the Thai border crossing at Kaen Teo and north to Sainyabuli, where buses leave for other northern destinations, including the old royal city of Luang Prabang.