The absolute theoretical quickest is to pick Honor + Warrior Code and use the general to put a citadel in melee range of that said city. It will even kill units from inside the enemy city, which are otherwise impossible to attack. Works best with any civ except Venice.
Otherwise, it depends on the specifics, what difficulty you play, what civ you play, what civ the enemy plays and what Era is the war taking place in. For example if you're Mongolia or Arabia you have access to the most OP units who can shoot and retreat in the same turn without any promotion. If you are Assyria or The Huns you have access to 2 good units who help to capture cities early in the game.
Americans capture cities quickly when they get their B17 bomber. England can put a city under siege from afar using Longbowmen who are much better than Crossbowmen at this task.
The "laziest" and most effective way to siege cities is using Artillery and their upgrades since they get indirect fire and have high range. This is a huge improvement over their corresponding siege units from earlier eras.
Of course, siege units are made for the purpose of attacking cities and sometimes they are good to use, but generally people don't use siege because of the disadvantages it has compared to normal ranged units. They are more vulnerable, less mobile, less strong vs normal units and get no defensive terrain bonus and that includes forts and citadels.
On sea, getting Frigates works very well, later Battleships attack cities at 3 range too. Keep in mind that Galleas/Frigates need only 60 XP to get range promotion so if you get all the XP buildings and either 1) build Brandenburg Gate or 2) get autocracy ideology tenet lvl 2 for military XP, they will come out of the city with Range promotion, and you can easily attack cities and units from afar. Getting range promotion will however delay obtaining Logistics so you should keep that in mind, sometimes it's best to go for logistics because it really increases unit power.
