Hello,
First, sorry for my english, i'm not used to write in this language...
Cities, roads and farms work in the same way : you are not allowed to place a meeple on a zone (city, road or farm) already occupied by any player (even you).
So, if a city is occupied by a meeple, you can place a tile to complete it, but not a meeple. By doing that, you just virtually add points to the city's owner.
If you want to "take" a city, you have to place a meeple on another city tile around the first city and on next turns, try to assemble them with other(s) city tile(s).
Here is the interest of the big meeple, which counts for 2, and allows you to score all the city points if your opponent had placed an only "usual" meeple.
For visual explanations, see "Special cases" on the base game page on Wikicarpedia.
Good game !