my military production is zip

That usually indicates that you don't have any military funding or you don't have a starport built.  You need at least 1% military funding (or Focus on military on a planet) to build ships.

Open your ledger (F4) and drag the sliders for military, social and research around (note that their position does not always reflect the actual percentage, they're wonky that way).

I had my military slider about 1/3 up. I cranked it all the way and that got my military production going on Earth. I thought maybe I needed a recruiting center for military production...but it's a starport, eh? I guess that makes sense since building ships is the main (the only?) military thing to do. So then the more military production, the faster I can build ships, I assume.

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Once you get a starport up, and start a given ship, yo can play with the sliders in your economic screen and then see what it does to your completion times for that ship.  I found it gave a real good feel for how you were affecting military production.  My understanding is that it also depends on manufacturing boosts such as factories and asteroid mines.  Not too sure about how much population affects affects ship manufacture, but it seems to for me.  Others will probably have more accurate formulas for the whole thing.

Planetary population has no effect on manufacturing.  It's just the structures on the ground and anything you get from asteroid fields and economic starbase boosts.

Also, your total spending slider is a factor.

That is, a planet's military production (excluding asteroid stuff) is a multiplication of (your total spending), (percentage applied to military), and (the sum of your on-planet facilities).  Thus, you could be spending very little and have the percentage slider 100% the way to military and get little or no military production.

Also a factor is the state of planet habitability.  If you cannot colonize the planet (say you capture/trade for a toxic planet though you cannot colonize it), then the factor will be zero.  If you have half the colonizing tech, then 0.5.  If the type is your native type or yo have fully researched it, then it is 1.0.

Thanks to all for the information. LTjim, I was confused by the 50% research thing. Now I understand.

From the two explanations, I am hearing that population may indirectly affect military production.

More population = More taxes = More spending = More Military spending from slider

All that is then combined with the calculations for on planet buildings and asteroids, which do not depend on population.

Is that correct?  I ask because I see military production inching up in increments smaller than I can account for otherwise.

Indirectly, yes, if you mean total Empire population.

However, you could get the same mil production no matter what the population was on any one turn.  With more tax income, however, you would be better able to sustain it.  Once you go enough in debt (400?), all production stops until you're back below the debt ceiling.

My point is that mil production itself is independent of pop.  More pop does mean more tax revenue.

The debt ceiling is 500bc, if you're at -500bc or lower, all production ceases except some focus production!

As stated before, population has no direct bearing on production, it only determines your income but doesn't determine your military expenses as taxes are not tied to expenses (it does factor in at your maximum espionage budget though). You can run all your factories at full production regardless of whether you have the taxes too offset the deficit, it's just that as soon as you hit that debtceiling, the plug is pulled...

I also believe I remember reading that you're only charged for half of asteroid production contributions and that moons and starbases are a 10% or 25% 'free' bonus or something?

You are charged fully for asteroid production. Bonus production from moons and starbases works like all other bonus production: you are charged only for 50%.

Asteroid mines do add to your manufacturing capability (mp) on a planet, but they don't provide a percentage bonus like power plants, moons, starbases and your race's military and social abilities.

Any percentage bonus to your base manufacturing ability (initial colony + factories + asteroids) is costed at half what the base manufacturing points cost.  Same goes for bonus research (in fact, these are rolled together in your finance screen).

Effectively, the more percentage bonuses you have going on, the cheaper it is to hit a particular level of manufacturing or research output.

Some of the bonuses are civ-wide so they're not shown on the planet screen.