Ok, after looking through what's been done so far, I think I'm going to start at the beginning: pulling the relevant formulas out of the demographics article so that they're all in one place for reference. Which should make it a bit easier for people other than oyzar to draw conclusions in future.

But that does mean I might not get to the summary today.
GNP
gold income + culture + espionage + (research*bonus) - expenses
MFG
total hammers, including unspecific bonuses (i.e. forge bonus, but not the expansive bonus, which applies only to workers)
Crop Yield
total food from worked tiles
Soldiers -- several factors go into this sum
Population
1000 for every other total pop point (i.e. at 2, 4, 6, etc)
Technologies
2000: Sailing, Hunting, Mining, Animal Husbandry
4000: Wheel, Alphabet, Astronomy, Metal Casting, Compass, Construction, Steel, Radio, Satellites
5000: Composites, Stealth
6000: Mathematics, Chemistry, Combustion, Archery
8000: Guilds, Fission, Flight, Bronze Working, Machinery, Assembly Line
10000: Horseback Riding, Iron Working, Artillery, Industrialism, Rocketry, Advanced Flight, Laser
12000: Gunpowder, Rifling, Military Science
Improvements (unused UBs omitted)
2000: Walls, Dry Dock, Forge, Factory, Stable, Mint, Assembly Plant, Industrial Park, Levee, Dike
3000: Barracks
4000: Mt. Rushmore, Red Cross, Iron works, Statue of Zeus
6000: Military Acadamy
8000: Heroic Epic, Chichen Itza, Scotland Yard, West Point
10000: Great Wall, Cristor Redentor, Moai Statues
Units (unused UUs omitted)
2000: explorer, warrior, galley
3000: archer, trireme, caravel, carrack
4000: spearman, holkan, chariot, immortal, galleon, airship
5000: catapult
6000: swordsman, axeman, pikeman, longbow, horse archer, east indiaman, privateer, guided missle
7000: crossbow
8000: war elephant, trebuchet, frigate
9000: maceman, musketman
10000: knight, ship of the line
12000: grenadier, cuirassier, cannon, ironclad, fighter
14000: rifleman, redcoat, anti-tank infantry, machine gun, missle cruiser
15000: cavalry
16000: transport, carrier, bomber
18000: SAM infantry, artillery
20000: infantry, stealth bomber
22000: mobile SAM
24000: jet fighter
26000: gunship, mobile artillery
28000: marine, submarine
30000: paratrooper, tank, destroyer, stealth destroyer, attack submarine, tactical nuke
32000: mech infantry
40000: modern armor, battleship, ICBM
Land Area
Land squares within borders, times 1000.
Population
Sum of all your cities taken individually, using:
1 pop = 1000
2 pop = 6000
3 pop = 21000
4 pop = 48000
5 pop = 90000
6 pop = 150000
7 pop = 232000
8 pop = 337000
9 pop = 469000
10 pop = 630000
and so on. The formula for each city is [pop^2.8], rounded down.
This thread has a calculator, which I haven't tried out.
Approval Rating
Total happy faces divided by the total of happy and unhappy. Initial default is 50%.
Life Expectancy
Same as approval rating, but based on healthy faces and sick faces. Initial default is 30 years.
Imports/Exports
Won't come into play until we have trade routes, but basically it's how much money your trade routes are making for you versus how much money everyone else's trade routes are making for them. A higher ratio is ranked better, regardless of how much total money is involved.