I tend to be a defensive player and it took me a while to be comfortable with aggressive expansion, which is the key to Deity, at least in my experience. I think I played a dozen with Russia before winning at Deity. What I learned from Russia, and a few other civs, is how to expand somewhat quickly but not so quickly I cannot keep my cities strong. The AI gives about a 20 turn grace period during which I expand aggressively by building two or three warriors, switching to food tiles to grow my city to 3 pop, then building a settler in five turns. Around or before then I usually get the free settler also. This gives me three cities early. One is always a science city. The second new city can be anything, depending on what the map looks like. If I see a sweet production site inland, I settle it early, build barracks and let it grow. One of the other cities pops another settler for a second science/gold city. Sometimes I catch up quickly in science and pull ahead. Other times, depending on what civs I'm in with, I don't.
If the AI civs are nearby, aggressive, or Germans, I may fall into a defensive struggle. I always try to establish a strong city with good production forward, or a chokepoint, to take the hits, behind which my other cities can continue to build. Islands are lovely, and if I can, I settle one, build a settler, settle the next, and so on. Mainland, chokepoints are very effective when manned by the most current units, and are also good fun. In one Deity game with the Spanish, I took advantage of a natural chokepoint and kept three AI civs at bay by continually replenishing my little stone fort with pikemen, riflemen and, eventually, tanks. It was hilarious watching the AI stack archer and legion units up endlessly. My stalwart troops upgraded until they were invincible. No one ever got through and my two mainland cities kept cranking the production (East India Company, cathedrals, etc.) while my island cities cranked science and gold.
I find that if I play smart and focus on building both good defense (which includes siege units in the cities) and powerful infrastructure (gold and science buildings in their respective cities, good production, sufficient culture), I can come back late in the game. Big time. My cities outcrank AI cities. Games where I fall behind, then come back, generally end in an economic victory because some other civ, usually the Romans or French, is too far ahead in culture, leaving me few wonders to build--but there's still the World Bank. I've become very fond of being extravagantly wealthy in Civ Rev.
