So the trick is probably:
- know what to tech
- strong build order early game
- 3-4 cities = a big plus
- good diplomatic skills
- no nearby warmongers
- large populaton, lots of farms
- lots of gold (you need it to prevent war and to prevent other nations from winning the game before you)
- luck
It's possible to win with a warmonger next to you; you just have to be willing to go to war. Hear me out.
I just finished an Immortal science game as America. It was continents, and I was sandwiched between France to my west, Assyria to my east and Austria to my north (ocean was south). France had no other neighbor and sent his trade routes away from me. He was also bright red for coveting my lands. The others also coveted, but were dark red and had difficult terrain between us.
So I built two archers early and Dow'd France around T45. I also forward settled on him. I took a worker, and he sent his whole "army" after me, which was 3 warriors and an archer. I killed them and started harassing Paris. I pillaged his farms, took a settler and took another worker.
He never recovered, and I never made peace. I got NC around T90 (a little slow for a science game I guess) and I slowly built up reinforcements around Paris. I went in for the kill with 5 comps, a spear and 3 catapults. Lost all 3 cats, but took Paris as my 4th city.
You might not cap the civ on Diety like I did on Immortal, but harassment can cripple an opponent who you know hates you anyway.
Oh, and Assyria DoW'd me too with a huge army about 3 turns after I got Paris. I killed his army and got a 750
peace deal. Austria put a bunch of units on my border shortly after that, but I used some of Assyria's money to get Germany to DoW her.