OK, making the wild assumption that Stardock Central is working for you...
1- load SDC
2- do whatever registration you need (hopefully none...)
3- select "Software" from the top left, and then the Drengin.net tab. You should see GalCiv and a few other items listed.
4- go to Tools --> Settings and check the "Show application revisions" box. That will let you see exactly what version of GalCiv you have installed.
5- click on the GalCiv listing in the main screen... an "Update" button should appear to the right of it.
5a- if no update button appears, try Tools --> Refresh Application Data, as well as making sure you're connected to the Atlanta server (Tools --> Settings --> Connection). If that still doesn't work, try restarting SDC. And if THAT doesn't work, go make noise in one of the myriad download problems threads around here.

6- click Update.
6a- the file should only be around 1MB. If it's 85MB, SDC is downloading the whole game. Return to 5a.
Good luck!
- Ash