I am trying to learn Deity level as well. Here are some useful tips for novices:
0) Expand fast. This helps on all levels, but is critical on Deity level. Practice the early game, experiment with different starting build queues. A high power rating makes everything else easier. A low power rating makes everything else that much harder.
1) Check the trade screen every turn with every civ. Experienced players can get a feel for when the big trades will be available, but novices need to get in this habit. Missing one trade can make it that much harder to catch up.
2) Set research to zero or 1 gpt. It is cheaper to buy techs than research them yourself. The exception is if you only have contact with one civ.
3) In Civ 1.29f buy workers anytime they are available. At 30 gold they are a bargain and weaken the AI. At PTW prices (about 80 gold), think before you buy.
4) Learn to trade. In Moonsinger's practice session on the GOTM board, the key turn is the first turn an AI learns Mapmaking. On a standard map this may be around 2250 BC. Stay alert, because if you miss it, it is that much harder.
http://forums.civfanatics.com/showthread.php?s=&threadid=54088
5) Learn to stir up wars. The AI has tremendous production capacity. Getting them to fight each other is a way to bleed that off. It is also a good idea to seek allies, or join in when a war starts (piling on).
6) Send early units exploring, use the luxury slider (F1) to keep citizens happy. Your world map will be one of the most valuable trading commodities if you can get Mapmaking from the first AI the turn it is discovered. Early exploration is key to making it valuable. Barbs can be a problem, but their setbacks usually will not be as valuable as a decent world map and contacts from early exploration.
7) Give in to enemy demands. Almost always the way to go on Deity. The rare exception is if you are ready for an offensive war.
8) Learn how to do mass upgrades:
Warriors->swordsmen->medieval infantry
Chariots->horsemen->knights->calvary
Mass upgrades are often the most efficient way to construct an offensive army.
+ Bill
I know there is already a thread for short tips but its very exhasting looking for specific Diety Tips, so please post any Diety Tips here. This will be very helpful 
. (For me too)
