Where to start, as tenngun says, there are so many good ones.
For a really good history of the Ashley-Henry partnership and Rocky Mountain Fur Company, and a very entertaining read, I recommend "Majority of Scoundrels" by Don Berry.
Chittenden's "Fur Trade of the Far West" has been in print since 1902, for good reason.
Those two will give you a good background on the basics of the American fur trade of the far west. I reread and refer back to them all the time.
For a day to day look at the average mountaineer, Osborne Russel's "Journal of a Trapper" can't be beat.
For a look at the southwest fur trade, try Ruxton's "Life in the Far West" and Garrard's "Wah-To-Yah and the Taos Trail". These last two really capture the speech patterns and attitudes of the mountaineers, and are good easy reads.
There are many, many more, but these will get you started.
Rod