Intermediate Colony Management Guide - 0.95.1a-RCC6
Colony Management is no longer in the game. You can manage 5 colonies instead of 6. The rest of the information in this guide is still accurate.
tl;dr - pick worlds that can be specialized, stack your worlds so that they produced the maximum amount of those resources, max your stability and accessibility
This video explains most of what you need to know about managing multiple colonies. One thing I forgot to mention was that the way you gain additional stability is from buildings like battle stations, ground defenses, patrol HQ, etc.