Please make sure that your OS is up to date. Especially, if you are using Windows 7.
Then please go to https://www.microsoft.com/en-us/download/details.aspx?id=48145 , click on the red "Download" button, then:
if you are using 64bit operating system download both "vc_redist.x64.exe" and "vc_redist.x86.exe", or
if you are using 32bit operating system download only "vc_redist.x86.exe".
After the download is complete, install all of the downloaded files. Please make sure to run the installation as an administrator. To do so, right-click on the file and select "Run as administrator" from the drop-down menu.
If for some reason you can't install aforementioned updates or redistributables and you meet the requirements, please check in programs and features, if you have them installed. If you do, use the uninstall button and try installing them again.
After the installation process is complete, GOG GALAXY should work properly.