Social production works mostly under the same rules as the Military production and is spent on projects. Amount of social production is set by moving sliders on Finance management window, and is represented by hammers on the Colony Management screen. Each hammer represents 1 bc worth of output, i.e. you are paying 1 bc for each hammer. If the hammers are in parenthesis it indicates that no projects are queued. In very early versions of the DL game (before 1.X) the player was charged for that "empty" production anyway. All later game versions and expansion packs transfer those unused hammers into military queue. To be used there, the military spending rate must not be set to 0%. If a planet doesn't have a Starport, or doesn't have a ship in starport's building queue, those hammers remain unused, and player doesn't pay for them.
Bonuses are applied differently to the production depending upon where the bonus comes from. For example, if your planet has a moon then you receive 10% bonus to the maximum possible number of hammers. You will still need to pay credits for each hammer you are getting from this bonus. The same is true for tile bonuses. If, however, you have 10% social production bonus as your civilization bonus, then you will get 10% hammers on top of the money you paid for the hammers, i.e. you get "free" hammers. As of v1.1 Beta 3 though, 50% of production/research bonus is free, the other half is still paid.
Please check Military production on how production works in GalCiv-2 expansion pack "Dark Avatar".
In TA (not confirmed yet for DL & DA) bonus production is only generated for social production if there is a social project queued. For example, if you have 10 hammers and gain a 10% bonus to social production you'll generate 11 hammers. However, once all improvements are finished the planet will drop back to 10 hammers losing the one hammer gained from a social bonus. In effect, this prevents bonus hammers being turned into bonus shields.