noob needs help

1) Research and create a Broadcast Center/Media Hub/Temple of Communion (depending on race) to spread your culture to nearby planets. This will increase your allegiance cap by 10% and increase the rate at which your allegiance rises to that cap.

2) Set your homeworld to a more central location in your empire. Allegiance is measured by distance (in phase jumps) from your homeworld.

3) Research the tier 8 civilian upgrade for the Advent which directly raises your allegiance caps by 5% per level (maximum gain of 10%).

Build a culture building (Broadcast Center, Media Hub, Temple of Communion) either at or near the planet. Those buildings generate culture, which will raise the allegiance at the planet you put it at, then spread to nearby planets (phase lanes change to match your empires color to show the spread).

That will raise the allegiance to the planets cap, which is shown if you mouse over the allegiance thing with the planet selected. The cap is 110% for your capital, and goes down as planets get farther away. There's only two ways to increase the cap:

1. Advent have a technology to increase the cap.
2. Move your capital planet (its good to have it in a spot where its central to your planets).

How different is the impact of the culture buildings if it's at the planet versus 1, 2, 3, or more systems away?

If anyone knows the answer to my last question, I'm really curious. Thanks.

Moses, there are several differences. First the culture building uses up logistics slots. Second, your culture spreads much slower once your outbound culture reaches and passes through a junction point gravity well. Each planet your growing culture passes through reduces its spreading speed - which is why you want culture buildings near your frontiers. Third, for the same reason, it's also much easier for the culture to be pushed back by capital ships stationed there. Other than that, there's no real difference.

-- Retro

In terms of allegiance, the only difference is that it goes up faster the closer your planet is to a source of culture. The cap doesn't change, and any planet within 2 hops of a culture building will get to the cap eventually (so no need to spam broadcast centers).