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.