A really cheap way to win is to turn on Raging Barbarians, using a leader with the Barbarian trait (where no other leader has this), and a nice, open map (with lots of Ruins/Barrow spawning-terrain), so that everyone else gets swamped by barbarians, and the output of Ruins and/or Barrows. The only thing you have to do is not declare war on the Barbarians; pretty much anything else you do is irrelevant.
More seriously, I find that it's just a matter of seizing a number of advantages that you get at lower levels - abusing Slavery/Sacrifice the Weak for production, abusing Bloom/ Chop down Forest for production, using spellcasting units far better than your computer opponents, knowing the AI well enough that you know what they'll do next turn, and can make plans in response, only engaging in war with overwhelming forces (or at least enough to divert any potential counterattack to defense), using terrain well, better city development, better promotion strategy, aggressively using large numbers of expendable (summoned/Fireball/Meteor Swarm) units, better early city creation, grabbing multiple religions, excessively trading for technology, razing less important cities, while capturing more important ones, using terraforming properly, using water units better, etc.
The reality is that with the weaknesses of the AI, it should be fairly easy to shut out opponent after opponent even with a large disadvantage. Don't be afraid to turn all your opponent's terrain into Desert, and/or pillage every tile, if that's what it takes to defeat them. In any case, you're the only one going for a win, so at worst, make/buy peace with everyone, and go for a cultural victory.
Also, I should note that if you're really having difficulty, you can alter Monarch in CIV4handicapInfo.xml to be in between the present Monarch and Emperor levels, to give you a bit nicer of a gradient.