Are you playing with Beyond the Sword expansion pack, or Warlords?
I suck at military too, though I've been trying to get better. Though I'm a beginner at warfare, having spent my civ years with cultural victories
maybe I could help a bit.
I begin with building units at the very beginning now. I don't think that you need granaries, libraries and monuments in general when you're planning a warlike game. I first build a worker, then a warrior or workboat while waiting to get to size two then try to chop a settler quickly. I think you should try some early rushes, they're awesome! If you're planning on one, then you should choose your civ and research at the beginning carefully, like getting your first settler right after bronze working so you can settle near it as soon as possible. I learned a lot from guides here!
My favourite is the Roman Praetorian rush, even though IW is expensive at the beginning it really pays off.
Just get barracks, workers and settlers at the beginning and then get out as many units as you can. Don't wait too much and try not to attack creative civs without catapults, it gets ugly.
Slavery is great for getting units out fast, so bronze working-slavery-chopping and lovely Praetorians with City Raider promotions are a great combo for me at least.
Happiness seems to be an issue with you, so slavery would be great for whipping the unhappy population. Try to stop growth when the city's reached the happiness cap by changing the tiles the city works. I now work hills and mines when I want units fast and not farms, since the extra food doesn't really help. Cottages are great since maintenance soon gets to you.
After wiping out one civ with the early rush (Even I manage the early rush easily now, since the AI just have archers and maybe a few axemen if you're quick) things get much easier. I just continue with units and don't bother with other buildings, since you can easily demand the techs when you're so powerful. And if you have a city with lots of food working a few scientist specialists really help. When you get a scientist build an academy with him in your wealthiest city, so you can build lots of research. I don't care much after gunpowder anyway lol. Make sure to scout the territory first since I lost a lot of turns at first searching for the citiesi and possibly end up on the other side of the river. You need to get there as quickly as possible since the AI will whip units.
I hope this helps in some way! I'm relatively new to warmongering too, but I got pretty better in a quick time. Good luck and hope what I wrote makes sense