As far as I know there's no guide on culture, but here are the key points of it

- Culture spread affects max allegiance, and allegiance gain/loss. Each planet other than your homeworld loses max allegiance the farther away it is from your homeworld, resulting in lower income of credits and resource mines. Having friendly culture increases max allegiance by 10% across the board (up to 110% on homeworld), resulting in an increase of revenue. The more friendly culture you have spreading, the higher your planets' allegiance will increase, and the more hostile culture the faster it will decrease (allegiance gain/loss is capped to .05 per second)

- Races get benefits under friendly culture with research. The TEC gain faster antimatter recharge, Vasari gain damage bonuses, and Advent get shield mitigation bonuses under the influence of friendly culture. There is no penalty for being under the influence of hostile culture, just no bonus either.

- Capital ships push back hostile culture, either from your owned planets, or neutral planets. The rate of culture push back increases as your capitals gain levels.

Let's take a quick example:

Your border world generates 10 culture/sec, and the enemy's right next door generates 12. That means he's winning a culture battle, and eventually your world will be under influence of his culture, and its allegiance will start dropping. Because the difference is only 2 culture, it will probably be dropping by .01 or .02. If the difference was higher, it would be dropping faster (but, again, cap is at .05). When allegiance reaches 0, the planet rebels and turns neutral. If it's still under the effect of hostile culture, you will not be able to re-colonize.

Say you have 4 capital ships, each pushing back .5 culture/sec (the exact amount is listed in the infocard). If you move all 4 to that border world, you will push back 2, and along with the generated 10 you'll equal the enemy's output of 12 and neither will lose allegiance.

Hopefully this makes sense The numbers I pulled out of thin air for a quick example, and feel free to correct me if I'm wrong!

Well, your race gets a buff in its own culture once you research the culture techs (always stem from the broadcast center research), and an extra 10% allegiance on each planet you own means an additional 10% income from every planet, which translates to a very nice economic boost.

Even if you're not interested in combatting your opponent with Culture, the techs are also what give you the bonuses for being in yours Plus, since they increase your culture output it will make it harder for the enemy culture to win over yours.

But yes, allegiance gain or loss is slow, it caps at 0.05% per second, and that's only if the culture gap is wide enough.