I tested this quite a bit in the Persia Civ if the week thread. There are 2 ways of doing it I recall. Physically move as mentioned, but this doesn't work for me if I'm 2 tiles away, and I can't remember if it works for taking a city. A better way is to use the attack hot key (see your key bindings to see which key, I think it is A) then click the city tile.