Also, depending upon what you're researching, the time difference might not be noticable. Building a single Discovery Sphere in my latest game only cut down my Tech Research victory's time by an extra week per upgrade from Invention Matrices.

Research is cumulative across your civilization, right? You build research labs, the more you build, the faster your research goes? If you build two labs on a colony, that's better than one, right?

Yes. Yes, and Yes.

Also, you can click the 'emphasise research' button to, one would think, increase research. I just clicked the 'emphasis' (or whatever it's called button, the options are 'military, social, research') on all 7 of my colonies. It had no impact on how long it took to finish my research.

Yep you can. I think the tutorial calls them focus buttons. Anywho.. I use them all the time. I make manufacturing colonies that focus manufacturing and have lots of factories. I do the same with research and labs. Social when you want to build infrastructure.. ie get those labs/factories built. The last comment its hard to tell due to not having the facts about your colonys. I can guess but I won't...

So what's the scoop here? I have my 'military - social - research' slider set someone in the middle. Research s/b easy to figure out (look for my future post on how COMPLETELY confused I am by manufacturing) so I'm trying to get it figured out fir

Beginning of the game I'd jack the social up to about 60%, other two at 20% for a while till those improvements get built. Later on when you aren't building improvements drop it down to 10 (0 if you are sure you arent building an improvement somewhere ) All the money will goto building ships and research.

This looks like a very cool game, but I am pretty confused about what to do here. Thanks for any research suggestions.

It is. Before I go, I'll leave you to a couple other sources.. the tutorial vids and the wiki https://www.galciv.wikicities.com/wiki/Galactic_Civilizations_Wiki. There is also a guide on the forums for beginner's help.. I'd definitely read that if you still have questions.

So, when you want to increase the speed with with you build something you emphasize 'social'?

Yes

When I start a game, before I build a research-lab I want to speed up my 'build-up' infrastructure to make the lab get built quickly. So that means build a factory, and put the slider at 'Social'?

Yes. To get things rolling even faster, you could just purchase the factory instead of waiting for it to be built.