When taking international buses in Asia, there is in most cases no direct connection, specially when the cities are not connected with a direct straight road. It's better to look for 2 or more connections to get you there.
Same in this case. You can take a bus from the Vientiane Central Bus station to to Khon Kaen:
Khon Kaen 08:15, 14:45. Price: 50,000 kip, 4-5 hours
and then from there another one to Chiang Mai.
Now when it comes to preparation and buying bus tickets in advance, you are out of luck. You are in a very local territory here and won't be able to reserve bus tickets, let alone in English. So you will have to make sure that you prepare yourself with some internet translation of the name of the city and the term "bus" as well as "ticket" on printed paper and use that to find the ticket counter and then to get a ticket.
At least you will know that there IS a bus, how often it goes and what you expect to pay for it.