Before Construction, you will need to bring higher numbers. Inevitably you will lose units weakening the defenders first before the rest of your stack can capture the city. If you can't field twice as many units as archers are in a city then don't attack yet and train more units.
After Construction it goes like this: use Siege/Spy to bring down the defense of the city, then you attack with some of the siege to inflict collateral damage. Then you use your city buster units to take the stronger defenders (be it city raider, or anti-whatever-is-defending), suiciding the lower leveled ones first if your strong ones can't get odds of +60%, and lastly you use the units that are closer to promotions or you want to level to take the city. Cavalry make good "last attackers" against non-hill cities because you can either move them in the city or let them defend the wounded (medic cavalry).
EDIT: It almost always goes like that unless your city takers get good odds against the city, in which I save the siege for later or to kill weak defenders for exp.