Really detailed breakdown of exactly how the numbers work? v3.95 or 4.0

I would recommend looking at the XML located in the main folder. You can find a lot of numbers in GlobalDefs. Otherwise, if you have specific questions we can probably help if there isn't a post already. 

quick basics:

Raw Production - gained from planet capitals (base and adjacencies), population (1 / pop), asteroid mines (0.5/mine as of 4.0, adjusted for the distance from planet), and some buildings.

Raw goes directly into All Construction, Research, and Wealth as a base number.  All Construction is further split into Social and Military production (both get the full base value of All Construction as based on Raw).  Buildings will add both flat amounts to each of these categories, and percentages.

So, for example, if you have 10.0 Raw on a planet, a Space Elevator with +3 All Construction, and a factory with +10% All, you end up with 14.3 All Construction as a basis.  If you also have a Starport with +4 Military production, you have 18.7 Military ( (13 All + 4 Military) * 10% All).  You also start with 10.0 Research and Wealth (buildings will add both flat and/or percentages to these as well).

Influence works similarly, in that it also has the Flat + Percentage, but is not based on Raw Production, instead your planet capital and influence buildings provide this.

You start with some Administrators.  Others are provided with certain technologies (governmental and influence), or by casting Citizens (and later upgrading them).

Tourism is a bit wonky, it is based on the number of influence hexes you have, adjusted for how many are connected to your capital planet, and percentaged out.  It is especially confusing, because some tourism numbers are a percentage of the total influence, and others are percent adjustments to that.  Best not to worry about Tourism quite yet, it is a bit confusing.

Hope this helps.  If you have a more specific question, I'll do my best to answer.

(edit) if you hover your cursor over one of the production boxes on the planet screen (Social Production, for example) it will show a list of all flat and percentage adjustments.  However, it is organized very poorly.  If you stare at that, add up all the flats, and all the percentages, it gives all the data.  But it is not organized well, and difficult to read.  I'd love it if they actually cleaned those tooltips up a bit (at least by grouping flats and percentages, with subtotals) but that might be a bit much to hope for.

Tourism:  I'm not certain if the numbers are exactly correct, but this gives a rough explanation of tourism.

The idea is, that there is a lot of space traffic going on through all influenced hexes.  Tourism buildings will attract this traffic, where they spend money on your civ's cheap plastic souvenirs.  

So, lets say you have a total of 100 hexes of space in your influence.  Only 60 of them are directly connected to your home planet (40 are disconnected, but eventually as influence grows, it will connect.  That's the goal with a tourism-heavy economy - expand influence and connect all areas).

So you have 100 hexes, + 60 which are connected to home.  That is a potential for 160 income.  Most tourism buildings give a 1% tourism rating.  This means, that 1% of the traffic going through your influence will stop and give you money.  That would be 1.6 per turn.

Additionally, you get boni from certain planets (aquatic, colonization events, etc).  These are also expressed as percentages, which is partly what makes it confusing.  So a 25% tourism bonus would apply to the 1% traffic tourism income .. making it 1.6 * 1.25 = 2.0

Adjacencies:

Building up your planets is how to improve all your numbers.  Each building has at least one "type" (Social Construction, Influence, Wealth, etc) as well as (usually) at least one adjacency type.  What this means, is that the buildings work in synergy.

So, for example, a Space Elevator

- provides 1 All Construction 

- provides an additional All Construction for each incoming All Construction adjacency

- provides an All Construction adjacency to all buildings next to it

Adjacency boni are also provided by special tiles, with the icons.  Hover on that tile to see what bonuses the tile gives (both on the tile, and to adjacent tiles).

So a Space Elevator on a special tile that gives +2 All Construction, and that has 2 factories next to it (providing All adjacency) gets:

+1 (its own standard bonus)

+2 (from the special tile)

+2 (from the factories)

for a total of +5 All Construction (this goes both into Social and Military construction - it is not divided)

In addition, the factories give a +5% each, +2% per adjacency.  Lets say the two factories are next to each other, and the Elevator - this gives each factory +2 adjacencies each, so they are both +9% for a total of 18%.  Not counting any other factors (such as raw) - just from these three buildings we get 5 * 1.18 = 5.9 All Construction.

Thanks Adam, that helps a lot.

Glad I could help.