Since you're still learning (we're all still learning) my suggestion would be:
1. SAVE
2. If you have something the 2nd strongest civ wants try to trade it very favorably to them in exchange for a military alliance against #1.
3. Give a GIFT to #3 regardless of wether they join you or not.
4. Then try both ways. I waged a successful, albeit long war against the Romans in Democracy, the war lasted about 120 years and resulted in the capitulation of the Roman Empire.
Throughout the war I gave concessions to my other two neighbours. I allowed the Egyptians a right of passage (which I didn't need) gave it to them for free.
I gifted the Greeks money in exchange for an alliance against the Romans. Then after taking the city that had attacked me a while earlier, I took a roman city that was landlocked in Greek territory. Once I took it I established a governor, sold off the cultural improvements (I'm striving for a cultural or diplomatic victory... just to try something different) then traded the city to the Greeks for some silly tech and silks. They could't believe their eyes!
I'm not sure if that had any influence in the fact that they actively helped me take down the rest of the Roman empire though they got no cities out of it. However every time I took a city I gave the Greeks gold. I dunno if it was necesary, but it felt so freggin' realistic...
As far as combat was concerned, I pretty much lost 3x what the romans did. And that seems plausible, considering I GOT the cities.
Alessandro