How do you repair ships?

As far as I know, ships repair themselfs over time. 

But if you have the money, you can upgrade damaged ships. If you save the same ship design with two different names, you can use the upgrade as a repair.

They repair faster in your territory and even faster when docked in a planet or shipyard, but even then the repair rate is very slow, especially for the larger ships. I think they need to change the healing rate to %max from a flat number and give docked ship healing a big buff.

OK, so I sent my seriously damaged survey vessel (the only survey vessel I've got at present) to one of my shipyards, and now the shipyard reports that it's being defended by one ship. However, I can't see the ship to either determine its status or to move it out of the shipyard -- the only evidence of its existence is that report from the shipyard. How do I get my ship back?

If you have a shipyard and a ship is stationed at it, then when you select the shipyard there should be an area on the right hand side of the selection details box in the lower left hand corner of the main screen which shows icons for each ship stationed at the shipyard. Click on the icon of the ship you want and you should see a dialogue menu pop up which says 'eject' and a couple other things, off to the right of the selection details panel. Click 'eject' and your ship should pop out of the shipyard. Alternatively, you should be able to click on the ship icon and then click somewhere on the main map to get the same effect.

If you don't see a ship icon in the selection details panel of the shipyard but you do see an empty box on the right hand side, hover your cursor over the area and see if you can find the ship. The box fills with ship icons starting in the top left and proceeding to the bottom right in the same manner as English text is normally written.

Found it. Thanks!

Is it just me (not having played GalCiv I or II), or is the documentation on basic gameplay a tad skimpy? Particularly given how complex the interface is?

It's not skimpy, it's effectively non-existent.

There is a Wiki but it is fairly new and not well fleshed out yet. I doubt your question would have been answered there.

I looked over the manual and I thought it was not bad, but there is, as you said, so much detail.

Forum is probably best until the Wiki gets up to speed