1. Faster-Than-Light Travel & Communication
Objects in space are very far apart, so this is an obvious requirement. Without faster than light travel, it would take too long to go from point A to point B, people would die in the interim and the goal of the effort would be forgotten.
2. Self-Sustaining Environments (Biodomes)
Not all environments will be friendly to the species attempting to colonize them. Terraforming is an option, but if functional biodomes can be constructed, terraforming is not necessary.
3. Industrialized Agriculture
Large scale production of food would be required to feed the enormous population required for a proper space empire.
4. Genetic Engineering
Genetic manipulation to create superior traits amongst all people, and mass-production style breeding would benefit a species looking to populate many worlds.
5. Standardized Education
To create the best possible race of people, everyone should be educated on a standard curriculum which maximizes intellectual development. “Classism” should be discouraged.
6. Repression of Religion & Other Intellectual Poisons
Religion is fairy tales, and has a detrimental effect on the minds of intelligent people. It uses the potential of an intelligent mind against the host. All kinds of intellectual poisons should be eliminated at the outset.
I am intentionally leaving militarization out. While it’s true that military power might be required in a populated universe, at present we have no evidence proving the existence of other life in the universe, which makes military power a waste of resources. The only thing a military is good for when you are the only intelligent race is to kill your own people, which is not a healthy behavior for a species looking to dominate multiple worlds.