As Moosetek says you can use ships to move pop from high pop to low pop worlds or you can do things to increase either that particular planets approval or your overall morale ability (i.e. Native Ability).

Or even more simply, you can do nothing. Once a planets approval hits 40% the pop on that planet stops growing and the planet's approval stops declining. The only real downside of low approval is that if you have a higher form of government then you may lose an election. However you can keep track of upcoming elections under the Government & Ethics tab in your Civilization Manager screen and simply reduce taxes during the week of the election.

However the intertwined relationship of population, taxes, morale and approval is central to this game and is far more complex than can reasonably be discussed in a single reply. You definitely need a deeper understanding of this topic to advance in this game. A good place to start is the GalCiv2 Wiki.

https://www.galciv.wikia.com/wiki/Approval
https://www.galciv.wikia.com/wiki/Tax
https://www.galciv.wikia.com/wiki/Population

You should probably read through the above links. Undoubtedly you'll have more questions so feel free to ask, but as a start you need to be very careful about building any farms on your homeplanet or more than one farm on any colony.

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After reading the above links the key thing to understand is that a planet's "base approval" is solely determined by the planet's population. The base approval is expressed as a fraction that gets smaller as the population increases. The importance is that the base approval also multiplies all other sources of approval such as entertainment buildings on the planet and native ability. So as a planet's population increases the base approval decreases which in turn decreases the effectiveness of all sources of approval increases.

For example a Virtual Reality Center (VRC) gives a 40% morale bonus. However the net effect to approval is determined by base approval which from the Wiki article is 0.91 at a population of 5B, 0.4 at a population of 20B and 0.2 at a population of 25B. So a VRC gives a 36% approval boost to a 5B planet, a 16% approval boost to a 20B planet and only an 8% approval boost to a 25B planet. Also note that the base approval numbers in the Wiki article are for DL and the DA numbers are even worse. I think in DA it's 0.2 @ 20B and 0.1 @ 25B. Plus in DA there's a cap on the net effect of native ability (i.e. the product of base approval times native ability is limited to 100%).

This makes getting a planetary population over 20B virtually impossible.

Like I said this is a very complex topic.

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Also there is one other important bonus to approval versus morale that's often overlooked and that is the 10% bonus you get for going neutral which applies directly to approval versus morale. Assuming that you keep a good protion of your planets at 20B this 10% approval bonus equates to a global 40% morale bonus. It's like a free fully populated morale mining resource. With the elimination of the MCC econ bonus in TA (and perhaps DA 2.0 as well) it makes Neutral a much more powerful choice.

The bonus you get for higher forms or government is not very great, only 10% for each of the steps from Imperial to Republic, Republic to Democracy and then Democracy to Federation, so this is not an early research priority. Also as I mentioned the time until your next election is listed under the Government & Ethics tab of your Civilization manager and reducing your taxes for the single turn of the election is easy to do.

The most important part about approval is how it affects population growth. What counts for pop growth is each planet's approval rate and not your overall approval. The above referenced Wiki Pop article goes into this as well. Basically you get a 100% pop growth bonus on any planet that has 100% approval. Since a planets income is determined by the planets population and your overall tax rate, the faster you can get a higher pop then the sooner you make a higher income.

There are three key approval numbers, 100%, 76% and 41%. Your pop grows at the basic rate on any planet with an approval between 41% and 75%. So there's no advantage of having 75% approval over having 41%. Same with 100%, if you can't reach 100% then there's no point of staying at 90%, you may as well increase taxes and drop your approval to 76%.

Generally what folks do is to try and keep approval high early in the game to get your population up on your colonies but once that's done they increase taxes which lowers approval to maximize income.

However game functionality is as it is and you either use it to your advantage or you don't, the choice is yours. As far as how it *should* work as opposed to how it does that's probably more of a prejudice on your part that is most likely due to how such things "work" in games with which you are familiar.

However, I do believe that to be a mistake. For example the way government "works" in the Civilization series is neither right nor wrong, it's simply the way it works. Applying what's right and wrong in the Civ games to GalCiv2 or vice versa isn't a valid comparison.

You'll find this game to be very subtle and complex with *many* different paths to victory all of which require in depth understanding of game mechanics to fully master. The point is that your ability to look at a complex system of techs and functionality and to choose a better, more efficient path, through them is what separates the good player from the mediocre. Just because a functionality exists doesn't mean it has to get used.

Take for example Industrial Sectors. In general I consider them to be a waste because their cost doesn't justifiy their increase in production. I think the smart thing to do (in many but not all cases) is to stop at Manufacturing Centers and not upgrade past this. Is this somehow cheating or is it the intelligent choice between options?

In any case there are as many ways to play this game as there are people playing this game and the only point of it is that you enjoy the way that you play. You have no more need to justify to me how you wish to play than I have to justify my choices to you. There's plenty of room for everyone.

I checked whatever documentation that I could find and didn't find any mention of the precise percentage benefit. I do recall it as being 10% and applied directly to approval versus morale, however the last time I played neutral was close to two years ago in DL v1.2 so I can't speak to anything since then.

I just did a quick check in DL v1.4x and am seeing the 15% increase specifically in moral ability (not approval) so either it has changed since v1.2 days or more likely I'm simply mis-remembering. Perhaps I was confused by the two different effects to approval of going neutral. The obvious one is the 15% morale bonus. The less obvious effect is that all improvable tiles are instantly terraformed adding the 10% high quality planet bonus to a number of planets that previously didn't qualify.

One effect that I am sure about was that once you changed to neutral you could suddenly crank up your taxes and start making some serious income. Plus you could do this far sooner than if you went evil, researched up through Concepts of Malice and then had to build the MCC before you started to get out of the cash hole.