I can tell you what Diety's like... it's EEEEVIL!

I can compete, but it's probably not the most fun difficulty level, mainly because the entire game can be decided by starting position, a small mistake, or a few bad luck rolls of the dice. If your starting position sucks (low food/production, only late-game resources), it's over. In fact, Diety almost requires you to move your starting settler to get resources with your initial town (fish, at least), risking either a 2-3 turn loss (oops, hello Elizabeth! You kinda caught me with my pants down!) or a reload (cheater cheater pumpkin eater!). The AI has so many bonuses that the standard starting (no resource) spot leaves you way behind.
If you survive the first few turns (not a joke), the game usually settles down for a bit. Survival is a matter of keeping the AI from deciding to gangbang you. It's important to realize why the AI attacks you:
1) Weak defenses. If you overexpand, or just try to squeak by with a bare minimum, the AI will eye your land like it's made of ice cream and sex. Try to keep a defensive army in each town, and focus on military techs to ensure your defenders are up-to-date.
2) You're in his way. If the AI can't reach an enemy, they rarely war with them. Conversely, if an AI player is next to you, expect a fight. When building cities, try not to put yourself between two AI players, you're likely to piss them both off and end up getting pinched, since even if they're enemies, they have to kill you to kill each other.
3) You're winning. The AI knows it's playing a game, and if it sees someone is going to win, they'll try to stop it. If that's you, you may as well be the love child of Hitler and Paris Hilton.
4) He just hates you. On Diety, you start the game having already ripped a chili-fed fart in a compact car with the AI. You have to be doubly nice to recover, and sometimes his grudge is just inevitable.
Other notes for people who need a hand:
When you make an army, only one unit (the one that creates the army, I think) counts for the army stats, so only 1 in 3 towns (roughly) needs a barracks. Also, always build armies - lone units are fodder.
If the AI starts demanding tech/money/people, it means he thinks your army is weak. That's a clear sign to build troops, form armies, and grab military techs, stat.
Don't be too proud to give in to some AI bullying. If you're already at war, giving in to another AI's demands is often worth it. Better to give away some cash or a tech than to become the meat in an AI sandwich.
Rush production often. Settlers and buildings are usually worth more than the money. Rush troops whenever needed, especially if you can form an army. Other than the free settler you get for reaching 100 gold, you never want to have much money early on. Spend spend spend!
Find a way to get a boat out early. It's hard to fit in a boat when you're frantically trying to keep the AI from murdering you, but on most maps there are tons of free bonuses to be had if you find them first. Early on, those bonuses are massive. Also, remember to send along a warrior with that boat, so he can kill any barbarians on the islands you find, for even more goodies.
Don't overexpand. It's tempting to fill all the land you can grab, but if you can't defend it, you're just building towns for the AI. Focus on the spots with the best terrain/resources -right-now-, meaning resources you've already (or are just about to get) unlocked, and terrain that doesn't require buildings to be useful (grass+trees). Also be sure the good terrain/resources are right next to your town, as it might be a long time before you can get a courthouse up. Even if it costs you "the perfect placement", each town you build should have at -least- one usable resource, one grassland, and one forest, or else it'll probably take so long to grow that it'll be useless.
Don't ignore the navy. The AI is very good at punishing landlubbers. A boat next to a ground battle acts as a support bonus, and the AI -will- use this. It's also excellent at sneaking troops up your soft and poorly protected backside when you aren't looking.
Don't ignore spies. Always have one (or more) in any city that will likely face attack, and always take one (or more) with you when you attack. Spies can greatly weaken defenders before an attack, and the AI will use them a lot.
I'm sure some of that stuff is obvious to some people, but it wasn't to me at first, so I thought I'd pass it along. The best part about Civ (and especially this streamlined version), is that practically every game teaches you something.
