You can fly to Chaing Rai on AirAsia. Take the morning or noon flight unless you want to spend the night in Chaing Rai. From Chaing Rai bus station there are very frequent buses to Chaing Kong. Like every hour, if not more frequently. I forget the price but it is practically free. I forget how long it took but IIRC it was an hour or two. At Chaing Kong take a tuk tuk to Thai immigration at the riverside for like 30 Baht, clear Thai exit immigration. Pay like 20 baht for a ride across the Mekong on a rickety looking motor boat that leaves "often" to Lao immigration at Ban Huay Xai. Visa on arrival is available. IIRC $30. Bring dollars because it is 1500 Baht if you pay in Baht. The border closes overnight at 6:00PM so keep that in mind time wise. It is all very inexpensive and relativity easy to navigate.

There is also an easy and relatively inexpensive tourist minibus service from Chaing Mai to Chaing Kong if you happen to be in Chaing Mai anyway. Ask a travel agent in Chaing Mai.