Thaton to Chiang Mai is about 180km by road and takes about 3 hours, but with some excellent scenery along the way.
You can take the boat from Thaton to Chiang Rai, which takes about 3 hours. There is a government boat at 12.30 and cost 350 baht minimum 4 people May 2012. You can also charter private boats.
From Chiang Rai to Thaton is an upriver trip, and takes about 5 hours.
The bus station is near bridge. Buses depart from/to Chang Phuak Bus Station in Chiang Mai several times a day with the journey takeing about 3 or 4 hours prices are around 90 Baht. The buses are usually easily identifiable with English information on them. Buses to Chiang Rai and Bangkok also run albeit less frequently, a journey to Chiang Rai takes a couple of hours and to Bangkok about 12 hours 890km. In May 2012 there was only one bus to Chang Rai that left at 3pm and you had to change in Mae Chiang.
From Thaton you can also go to Mae Salong, and on to the Myanmar border at Mae Sai where you can extend your visa.
