I just think it's so cool and I want some more information to feed my imagination.
With drills and pipes made of bamboo, of course. Bamboo is a really incredible material, the sort of perfect combination of sturdy, easy to use and extremely plentiful to give it a really central place in the history of Chinese artisan material. If you want to get a good idea of what it looked like, this website has some fantastic images, including old paintings, historical photographs and reconstructions.
That aside, it is important to remember that natural gas was not used towards the wide range of industrial purposes that it is today. Coal had something of a transformative effect on the Chinese economy as a whole during the Song dynasty, but natural gas was mainly harvested and used in Sichuan province in the southwest. Sichuan (the little green bowl at the edge of the Himalaya) is essentially a dried up ancient sea, which means it is rich in both natural gas and brine. During the Song Dynasty, natural gas was employed to evaporate brine to create salt on a massive scale and the salt was traded all across China. Perhaps most interestingly, the effect of the this boom in salt production seems quite familiar to those who are aware of the resource scrambles in the Old West. Han Chinese settlers, who were heavily concentrated in the Chengdu plains of western Sichuan, poured into the brine rich regions of the east, which was already inhabited by non-Chinese peoples. The usual mix of conflict ensued, and the eventual Chinese domination of the region was only accomplished after a couple centuries of fluid, seesawing frontier conflict. And even today Sichuan is a very diverse province, and quite distinct from the rest of China.
The ongoing series Science and Civilisation in China (began by Joseph Needham) is a really vital resource for this information. My information specifically comes from The Country of Streams and Grottoes about the highly complex frontier interaction.
If you are interested in ancient Chinese engineering, have a look at the Science and Civilisation in China series that was started by Joseph Needham
There are several volumes specifically about engineering and several more that have engineering content. You may have to consult a university library to see them, although I suppose there may be scans to be found on the Web.
The use of natural gas was used to extract salt brine and boil it to have edible salt. I just visited the Zigong Salt Museum in Sichuan about two weeks ago and I can give a bit of information. Natural gas was found in the area by Li Bing who also created the Dujiangyan Irrigation system. The Salt brine in the area is very high with about 50 grams per liter in some areas. While digging sometimes people would get sick (natural gas) and so it was thought to be bad spirits. Some discovered that it could be flammable and then it was piped into a centralized boiling area by bamboo pipes where it could be used in Salt brine extraction.
The wells started by just digging down to brine water, however it was found that the salt brine was more concentrated the deeper one could extract. Narrow bamboo drill holes became used with percussion drilling techniques that became more and more sophisticated. By 1830's they were the deepest wells in the world at 3,000 feet. The bamboo drills were highly advanced and there were many different techniques to correct a drill that went off course or if there was a collapse.
The salt drilling took a lot of capital and labor as they had to be manned 24 hours a day and required the building of salt processing plants to boil and refine the brine. Some of the first contracts in all of China were drawn up by merchants to pool resources and guarantee profit (salt was controlled by the state through exclusivity contracts). I suggest you read The Merchants of Zigong by Madeleine Zelin for more information.
A condensed version of the engineering books mentioned below is The Genius of China by Robert Temple. It's about 180 pages with many pictures and diagrams. An incredible book that puts western achievements in proper perspective. I read it about 20 years ago. Probably very hard to find now. It's really for the lay person and probably a much faster read then digging through all those engineering volumes. Given how China is viewed differently today then it was back in the 1980's the book deserves a reprint.
If you can get access, "Science and Civilization in China" by Joseph Needham. 15-20 volumes documenting almost all science and engineering topics in ancient China.
Cambridge Press
Can be found all over the internet