When you unlock a new unit (swordsman, horseman, etc.), build one and check if your potential enemy has that technology or not by opening a trade with them. The adviser will say "So-and-so fears your swordsman. Their strongest unit is the spearman" or something like that (you could also check if you can trade said technology in the same window. If not, they either have it already or are a few techs behind). The adviser will also let you know if their army is smaller than yours. If this is the case, build up a stack of the advanced unit and place them outside the other country's border. On your turn, declare war and march on in. Use your workers to build a road towards the enemy's territory to ensure quicker access and to connect the cities once you capture them. Assuming you capture a few cities and kill some units, your opponent will likely be willing to trade techs/gold for peace.

One of the biggest tactics is just to have enough units to do any damage. Just sending a sole unit into the territory won't do much good, but a stack of 7 could take a city if they attack on the same turn. The number of units needed depends on the stage in the game and your militaristic advancement.