By train
Until 2003, Kunming was accessible by rail from Hanoi, Vietnam via a narrow-gauge railroad built by the French. The Chinese section of this rail route has since closed for passenger transport so the best way to get down to the border is by bus to Hekou from where you can cross the border to Lao Cai and take the train to Hanoi, or by air from Kunming directly to Hanoi. One can take a train to Hanoi however via Nanning which is a safer option.
There is a railway from Hanoi to Nanning, Guangxi, and one with some sensational scenery from Nanning to Kunming. Another rail route reaches Kunming from central China via Guiyang, Guizhou, and a third one comes South to Kunming from Chengdu, Sichuan. All of these train routes offer spectacular scenery, with long stretches of bridges and tunnels.
Bus, By Thumb
There are multiple roads from Laos into Yunnan. It's not too hard to hitchhike, but it will take some time because of the often abyssmal road conditions and inept drivers. If coming from Luang Namtha, Laos, bus services are available to JingHong in Xishuangbanna, Yunnan. From Luang Prabang, Laos, a daily bus leaves at 7:00am for around 400,000 Lao kip. It arrives at the long distance bus station in Kunming very early in the morning the next day around 5 or 6am depending on the driver. The road conditions on the Laos side both from Luang Namtha and Luang Prabang are at times sketchy and definitely mountainous to cause some people discomfort but get smoother on the China side and are much improved from awhile ago.
From Vietnam, the border crossing is from LaoCai, Vietnam, to HeKou, China. The rail route from HeKou to Kunming remains closed, so the only public transport option is by bus. The ride lasts roughly 10 hours, tickets cost around ¥135 and departure times are as following: 8:45am, 10:50am, 12:30pm, 1:00pm, 5:50pm, 5:55pm, 6:00pm, 6:05pm.