By car
By car which can be rented in Chiang Mai 4 hours away and other cities. Mae Sai is 61 km from Chiang Rai on Highway No. 110.
By bus
By bus from Chiang Rai or Chiang Mai. Buses from Chiang Rai are very frequent every 10-15 min, cost 40 Baht one way and take about 1.5 hours, while buses from Chiang Mai take about 4 hours 210 baht one way. All public buses terminate at a bus station well south of Mae Sai, so you have to continue onward to the city proper with red songthaews waiting outside 20 baht per passenger fixed fare. The blue songthaews to/from the Golden Triangle and Chiang Saen, on the other hand, leave from a stand in the city centre a few hundred metres down the street from the border. The last blue songthaew that departs for Chiang Saen leaves at 2PM.
There are also day-tours taking visitors to Mae Sai, the Golden Triangle, and a couple of other places to see on the way as well. Tourist minibuses are more expensive around 800 baht for a day tour from Chiang Mai including lunch and, if fully loaded but this is not always the case, are much less comfortable. However, this is still an option worth considering, if you want to combine your visa run with a sightseeing tour through Chiang Rai province.