There are relevant variables like map size. Difficulty level may matter surprisingly little if the AIs fight each other. As a rule of thumb a good war should last no more then 15 turns. There are exceptions, but usually is preferable to win the easy wars first.
A typical war may look like this: You produce about 200 shields per turn, which is 2.5 cavalry per turn. Once you have something between 20 and 80 cavalry, some of which are simply knights upgraded to cavalry, you declare war. You ensure to have significant positive gtp and buy all other AIs into that war. Now, for the first 2 to 5 turns of that war you make sure to stay within your territory. It is not yet time to fight yourself. Give those AIs a fair chance to wear each other down. Once your enemy is reasonably weak you can mop that enemy from the map. Losing some units is very much acceptable if this means to eliminate the enemy faster. Minimize the amount of turns between you taking your first city and the enemy losing its last city.
One thing to keep in mind: AI is set to defend its capital more than lesser cities. Given that, taking the capital may not be your primary goal. That may matter if you are short on units. But if you have say 60 cavalry you are not short on units and may not have to worry about such details.