1) Find a bird shooting challenge.
2) Accept the challenge and the wager.
3) When the timer starts, allow it to run out and do not kill any birds.
4) The wager will then double.
5) Continue losing the challenge until you have no money left.
6) You will be given a set amount of birds to kill.
7) Wait until you see enough birds in the sky and accept the challenge.
8) Kill all of the birds and win the challenge.
9) Now, put on your bandanna.
10) Shoot the man you were wagering against.
11) Now loot his corpse.
12) Leave the area and take off your bandanna.
13) He will re-spawn sometime later allowing you to repeat the process and get unlimited money.

Here is a video tutorial: