How to add a domain user to Administrators group in Windows 10

To add an account as a member of the administrators group you need to be a local administrator already and you need to have rights to read the active directory information. A normal user can do this so what you want to do should be possible:

1. log on as local admin
2. connect on the VPN
3. open Start | Computer Management | Local Users and Groups (or run lusrmgr.msc)
4. double-click on the 'Administrators' group
5. click the 'Add...' button

At this point, because you are on the VPN and the machine is a member of the domain, you should be able to click on the 'Locations...' button and select the domain as the location of the user list. At some point an authentication dialogue should pop up and you will need to enter your normal domain credentials.

Daniel's answer is a little bit a clue, but it is too complicated (VPN). This task is pretty simple:

Computer has to be already in the domain.

1. open Start menu and find (by writing) mmc but don't run it yet
2. if you are logged as a user, click on mmc with right button and use Run as Administrator
3. Ctrl+M
4. add Local users and groups
5. select Groups folder and Administrators record (double click)
6. add your domain user account

PS: I'm using Windows with different language, if I named something wrong, please edit this answer and correct names, thanks.