These instructions for getting out of Kunming to the west are a little bit complicated -- but bear with us, they will take you right to Kunming West toll gate, prime hitching spot.
First, make your way to the Outer Suburbs Bus Station that's on Renmin West Road between Dongfeng West Road and Xichang Road. When you're there, you take bus Nr. 17. It costs a little bit more than inner city transit, but not more than around 12 Yuan. If asked where you're going, try your luck with "wo qu kunming dong shou fei zhan", which means "I am going to Kunming West toll gate"; this might help you to make getting off the bus easier. The spot where you get off doesn't seem to be a regular bus stop, so keep your eyes open for two very peculiar-looking SINOPEC gas stations; this is where you shout, dance, and do whatever else is necessary to get the bus to stop. You will first spot the gas station on the left, and then, maybe 100 meters further, a similar-looking one on the right. They look like huge tents standing on four massive concrete pillars and, really, can't be missed. Another landmark here is a toll gate a few hundred meters further in the direction the bus is going; it's not for you however. Once you've gotten off the bus, consult the map on the right to understand the walking directions better. You're maybe 10-15 minutes away from your hitching spot!
From where you got off the bus (marked with an (x) on the bottom right corner of the map) you take the first right, immediately behind the gas station to your right. You will walk with an orange brick wall on your left. From here you continue up the hill, keeping right. After doing a little semi-circle you come upon a little square with a basketball court where you take a sharp right and follow a path through a little neighbourhood of beautiful mud brick buildings. The path meanders and doesn't exactly go straight, but there's no obvious places where you could get lost, and after a while you hit a proper road. Here you turn right and find yourself crossing a highway bridge -- on the left, you can already see the toll gate. After you've crossed the bridge, you'll find the beginning of a little mud path on your left. Follow this path while keeping left, it goes in and out of a little fence and passes through a little settlement until finally you hit some kind of little stairway that takes you right down to the toll gate. Walk through the gate and exercise your itchy thumbs!
(Update August 2015 (by Sergey)
That gas stations already not working and soon will be destroyed, but for now you still can find the place where you have to get out from the bus. Bus ticket cost 7 yuan. You have to get out 2,5 km before Taiping, close to "Changpo" railway station. It's really easy way to reach toll gate. Check the link http://wikimapia.org/27985590/Kunming-West-Toll-Gate )
You can take a bus from the center, number 73 or A1 (and few more lines, but didn't remember all of them) until this toll gate https://goo.gl/maps/5531l (May 2015, this place is only visible on google satellite. It still doesn't exist on google maps. Don't get confused. Toll gate is there). You will see the toll gate from the bus on your right. The bus will stop 50 meters after the gate, so you have to walk back and ask people there. It's very easy and you should get a ride quickly. Be careful, this highway splits into 3 different directions after the tunnel. Make sure before you enter a car, to ask driver which direction he is going to. The best is if the driver is going at least to Anning. 3 km before exit for Anning, there is another toll gate. It's more convenient to try to find a longer ride there than on the toll gate described above because you will get lots of traffic coming from southeast of Kunming. (by NixyJungle)
Towards the Airport, towards the East: The rest of China
This is most likely not the best of options to get out of the city... but if you can't be bothered to research better alternatives, bus K9 can take you from the center to the eastern bus terminal for 1 or 2 Yuan. The terminal is less than a kilometer from a big highway ring that goes around the city, and from here you are sure to find a car (or several) to take you towards your desired direction. The spot where you will hit the ring also has an expressway to the airport. August 2017: this worked out, however, was really dangerous walking next to the highway for one km and also having to cross it! couldn't find a better option though... Once at the "right" place, car would stopped within 5min, but was even for the car rather dangerous...
Among others, bus 103 and 185 (?) can take you near a good on-ramp with a large toll-gate right before it. 103 departs from East Ring road, for example. Get on it in south-bound direction and wait until the bus has been going straight for a long, long time -- this is Caiyun North Road (yes, North). At one point, the bus will turn left at a big roundabout and then take the first right straight after. This is where you get off -- you follow the road that you turned onto from the roundabout for about 1 or 1,5 Kilometers and then hit the highway where you can hitch either at the on-ramp (worked fine in December 2013 even though works were happening) or at the toll gate a little ways back on the highway.