How was Rome able to conquer and rule a vast empire?

In addition, Rome was technologically advanced in both its daily life and in its military, so much so that there were few militaries on Earth that could resist them for long, at least as the empire was in its ascension.  Think of the US military now and the technology it uses, compared to most other militaries, and Rome had similar advantages.

Diplomatically, they were very sharp in how they dealt with other countries, as they took over vast territories even without war as nations and peoples realized it was better to be subservient to Rome than to be destroyed by them.  In many cases, being part of the empire brought more benefits than disadvantages, so there was an incentive to submit.  Think of how Puerto Rico is part of the US empire still, but does not want to become a state, nor declare independence, even though their culture and language are very different from most of the US.  There are benefits for them to be a part of the US without resistance.  Not the same, but the analogy works.