The March came about because Chiang Kai Shek and his German advisers decided to wipe out Communists strongholds in Jiangxi and Fujian. Their strategy was to encircle and crush, moving slowly and building fortifications. The Reds broke out of the encirclement and set off west. Eventually they settled in a new base at Yan'an in Shaanxi.
Exact numbers in various sources differ, but all say the journey took more than a year, covered several thousand kilometers mainly on foot, and crossed eight provinces. Over 80,000 men set out and not many over 10,000 completed the journey. Whatever else it is, the Long March is quite a tale of persistence in the face of adversity — climate, terrain and enemies.
There were several Communist armies which took different routes. map
The main Red Army
The main Red Army started in Jiangxi and Fujian and travelled by a very circuitous route to finally reach Yan'an in Shaanxi.
The second and sixth Red Armies
Other Communist units started in Northern Hunan, around Hefeng and Longshan, and went southwest. They crossed the path of the main army in Guizhou, then went on to Kunming and from there up into Western Yunnan (near the modern routes described in Yunnan tourist trail). They went north on a route more or less parallel to the main army but further West, passing through Gatze and Aba into Gansu, and finally linking up with the main army near Yan'an.
The fourth Red Army
The fourth army started near Tongjiang in Sichuan, went more or less due west to link up with other forces at Gatze, then swung north through Aba to Gansu. Once in Gansu, it split with some troops going to Yan'an while others moved west to hold some Silk Road areas and try (unsuccessfully, as it turned out) to connect with Russian forces who might provide arms and other support.
Following the route today
Young Chinese all learn about the Long March (of course, the official Party version) in school and some retrace its route, as in this news story .
Two British travelers retraced the route on foot , and wrote a book about it . The book was controversial; among other things, it claimed the route was quite a bit shorter than the 9,000 km in the official histories.
Some fairly expensive tours  with English-speaking guides are available.