There are 2 ways to conquer a city conquering and founding but it isn't that simple in some worlds you need to conquer it (send attacks for clear, then land cs, then wait and support) But in others there is a setting called revolt which we are focusing on today.
To take over a city in revolt world you need to attack it with a revolt attack which you unlock after researching conquest in academy ↓↓↓
Remember to always spy the target first to see if it is easy or hard and check if allies are near because if it is a professional alliance, they will try to stop it asap if it is a player they really need. Also you will need to clear the city first with offensive land units like slingers hoplites chariots horsemen (OLU) and clear the harbor with LS (light ships)
After you have done this do a revolt attack try to time it just seconds after your clear hits if possible and I recommend doing multiple clears also try to save your troops for the revolt attack since it makes it more effective.
When your revolt attack lands your units whisper bad rumors about the leaders of the city which makes city revolt (revolution happens) but when your units land and successfully land a blue revolt happens it’s a 12 hour period where enemy alliance still can support the city aka when rumors started spreading when this 12 hour period is over it tourns to red revolt and this is when you send your CS to take over the city when your CS lands if successful you have a new city . Red revolt also lasts 12 hours.
Remember: when there is blue revolt do not send CS enemy still can support the city so send more clearing attacks.
Try to do revolts with your alliance it makes it much much easier since alliance can help you both clear the city and support
Never send your CS with your attack you can put some offensive units with the CS just in case but never all of them!
here is one of the revolt guides i found in my alliance tab