While it is possible to enter Tibet from the east via Cheng Du to Lhasa, most visitors take one of two routes to Kailash.
Our route was to meet in Kathmandu, Nepal. From there we traveled by bus to the Tibet border at Zheng-mu and thence overland to Darchen, which is the departure point for the Kailash kora.
The alternate route, and the one by which we returned, is to fly from Kathmandu to Simikot in western Nepal, and then trek 4 to 6 days to the Tibet border at Sher, from which Kailash is a day's journey by jeep. It appears that many tour groups take this route, both entering and leaving, since we passed numerous groups on our return trek.
In previous years, Snow Lion had operated this trek in the opposite direction, entering at Sher via Simikot and exiting at Zheng-mu. Clients commented that after the 5-day trek, they were tired when beginning the kora. Thus, our route was an experiment in a sense. I believe that it succeeded for one very good reason: there is no gradual way to enter Tibet. Almost immediately you will be at an altitude of 12,000 feet or more, so acclimatization to the thin air is important to a successful trip. In our case, the 6-day drive from Kathmandu to Darchen aided this process, as we went from 4,500 feet to 15,500. In fact, our first campsite in Tibet was at 12,200.
To being the trek, it is necessary to get to Kathmandu. Since I wanted to use frequent flyer miles, I had only once choice from Atlanta: Delta to San Francisco from Atlanta, and then Singapore Airlines to Kathmandu via Seoul and Singapore. The total time in the air was 28 hours. In an attempt to mitigate the effects of jet lag, I decided to overnight in San Francisco, and then spend two nights in Singapore en-route.
Singapore Airlines flies to Kathmandu twice weekly from Singapore, so it was necessary to coordinate the other flights as well as the limited allocation of seats to award tickets.
From the U.S. West Coast, this route is reasonable. Others in our group flew via Europe and India, while one another arrived via Bangkok. It is a somewhat shorter route from the Eastern U.S. to fly across the Atlantic, although the total transit time depends on the connections involved. Snow Lion has a reservation service via Thai Airways for its clients, and promises good group rates. I cannot comment on this part of their services.