Complete the missions leading up to the establishment of the new Saints gang, including the escape from prison, freeing Johnny Gat, setting up the new gang house and Three Kings, in which you impress three possible high-ranking members.
An easy enough task. The missions act as a tutorial for newcomers, and will be a piece of cake for the more capable.
Thank you to d3nn1s99999 for correcting me on the proper manner of obtaining this achievement.