As stated in the comments, a city captured has to go through X turns of resistance before you can do anything with it, and its borders will remain at zero for that duration as well. There is an exception for recapturing a city that you originally owned (planted with a settler) but previously lost.
The duration is both on the map screen and the top of the city screen:


The formula for duration of resistance (which cannot be reduced by any game mechanic) can be found in the source code under ...\CvGameCoreDLL\CvPlayer.cpp
:
pNewCity->changeOccupationTimer(((GC.getDefineINT("BASE_OCCUPATION_TURNS") + ((pNewCity->getPopulation() * GC.getDefineINT("OCCUPATION_TURNS_POPULATION_PERCENT")) / 100)) * (100 - iTeamCulturePercent)) / 100);
In other words, there is a flat resistance duration plus additional time for each population point modified by how much culture you have in the city. Without mods, using the constants found under \Assets\XML\GlobalDefines.xml
, this comes out to be
3 + [Population] * 0.5 * (100 - [Your Culture]) / 100
So for most conquests, you will face resistance of 3 turns plus half the city size.