Sorry, but my previous post was a bit vague about improvements, so Ill have another crack at it. Im also trying to learn all the ins and outs of this amazing game, so please correct me if I've got it wrong.
Firstly, we need to clarify what improvements are as there are several different ways to improve a city.
1. Buildings.
There are the improvements that you build using your production shields granaries, barracks, temples etc. When you capture a city (either by culture or conquest) the game will apparently automatically delete all of these. So no free Culture points that would come with some buildings either. You may still find that there are some buildings but you will have caused them to be there due to the powers of certain Wonders - if you have them (e.g. if you have Pyramids it will automatically put a granary in all your cities, including the one you just captured). Check manual p101 for details).
2. Land improvements.
If the city had roads and irrigation you will get those for free. They wont be wiped. Unless you accidentally clicked on the wrong square and bombed them (been there, done that!).
3. Population improvements. This seems to be the least understood aspect. Despite what some people say they DONT all always rebel, steal everything or turn sour on you. A captured city can quite quickly be a great asset if you do it right.
Check other threads on overcoming corruption, unhappiness etc. but there are lots of factors, including what government you have, how far the city is from your nearest palace or Forbidden Palace, building a courthouse, etc Some of these can be brought into effect more quickly than others. But people who havent mastered the art of capturing cities in a useful way should maybe either raze them, or wait until theyre better placed (and believe me it can be done - some of my captured cities have become among my best producers).
One of the easiest ways to improve happiness might be by simply giving them access to your luxuries. No city gets the happiness benefits of the luxuries that you have on hand unless there is a road there. So put one from your captured city to the nearest point of your existing cities straight away (and if they are not already linked to each other they should be!). But while you are still at war with their native country they will also tend not to be as happy (understandably) so completing the take-over swiftly, or signing a peace treaty when youve grabbed a few good cities might be useful. Again, check the threads on keeping your people happy. And the manual page 115 onward has some info.
The reason most peoples captured cities go bad is probably that they have overextended their empire, and dont fully understand the rules of the game yet (at least thats why mine always used to go bad!). Not all the factors can be fixed instantly, and they can need a bit of settling in time, but if you get it right they can be great assets.
Hope this helps.
Cheers, Polonius.