Thanks for your comments and I see there is no easy ways to capture a city. It seems take a lot of effort/casulties to capture it.
A couple of lost units is usually of a similar cost to build as a new settler, particularly early on when settlers are comparatively expensive, so it isn't all that bad as long as you bring the right units to fight. And the extra bonus is you get to loot some money and take land and units off the opponent, making you relatively stronger. You may have to raze captured cities sometimes though, as expanding too fast can hurt you badly - you need to develop cash boosting technologies, and develop your cities commerce production so you can afford to have larger and larger empires, as well as the technology and units to defend it and expand it at someone elses expense.
How could you make your neighbor's city into a revolt? It happened to me once and the city just switched under my neighbor's rule without my neighbor declare war on me. I think it's a better way of capturing a city.
How would I do that?
If your cities are close together then the culture that naturally expands from each of your city (if you have any culture creating buildings, or other sources of culture being created in the city like artists, or setting the culture slider up, or the creative trait) and the opponents city will come into conflict. Whoever is creating more culture will tend to slow eat into the opposing sides land, and if that reaches the actual city it will mean that the city will have a chance of revolting - when it does you lose your defenses temporarily, your units get damaged, all production is stopped, and the city can eventually even swap to the opposing side without a fight (or even war being declared).
To do the same to the AIs cities, create buildings like monuments, libraries, theatres, run artist specialists, increase the culture slider (cuts into your money and/or research rate though), etc.
Later in the game you can use spies and espionage points previously spent on a given opponent to try and send his cities into revolt temporarily, which is another way to achieve the same thing, but you probably won't need to use that for a while.
I have another question. There are bunch of catapults and melee units in a group (within a box). Do each of the units get to attack the target within a turn? If so, they would greatly increase the damage on the target.
Yes, every unit acts on its own basically - you can group up a stack of units to move them together by double clicking on them, but you should split them again before you attack so you can choose which one should attack first (the button with the green dots showing arrows splitting the group up does this). If you hold (and don't release) the right mouse button on the units you plan to attack, it tells you the odds of winning (and retreating if that might happen), then return the mouse pointer back to the stack before releasing it to avoid actually launching the attack yet. Repeat this for each of your units, and that can give you a hint of which units are best to attack with at the time.
The other things to factor in are siege units collateral damage - if you attack with a catapult for example, then you can damage most or even all of the enemies units in one attack (it can hit up to 6 enemy units, but not enemy siege units). This softens the defenders up so the next attack usually has a better chance of winning, so this is why attacking with siege units first is so important if you possibly can. Sure, you will nearly always lose a couple - and for really well protected cities, sometimes quite a few - but it means all the rest of your units will then have a fairly easy time and should be able to take the city without too much trouble.
