If I'm going for a conquest victory, I tend to try and focus on researching the techs for siege weapons early. You can attempt to siege a city with just archers and melee units, but I think the city defensive bonuses make this a tough fight.
While you're working towards catapults, create some early melee units. Send them out to gain experience, and then upgrade them when possible, you'll have the backbone for a strong early game army.
In the very early going, I'd focus more on grabbing land and stabilizing your economy, so that when you make the shift to military production, you can still support your existing cities.
On the culture front, take the "Honor" track, and grab a Great General early. If you keep the General with your siege units, and properly protect them, you'll also have a significant advantage.
Being at war will mean you're sometimes on the defensive - make siege units for your border cities with your current enemies. One or two siege units can do devastating damage to AI armies, who don't tend to assault with enough strategy to avoid your siege weaponry. Sometimes it's even better to declare war, and then sit and wait for their armies - you can gain free experience and decimate their fighting forces with minimal effort.
Specializing cities also helps; this was something I learned late in my Civ4 days. Try to found your second or third city someplace with high production value tiles, such as hills and forest. Focus this city on unit experience and production speed bonus buildings. This will keep your war machine in good shape even into the mid and late game.