So the first question I suppose is, which device do I need to set as the VPN server (if that's the right term)?
My choice would be to set up OpenVPN server on your router (which I think you have already), rather than on the Synology Diskstation NAS itself.
An advantage of doing it this way is that after your relative logs on remotely, he/she will also be able to print to any networked printer you have at home, as well as accessing your Diskstation NAS. This very convenient when you need hard copy, but do not want to carry a heavy document while travelling back home. Printing in this way will not be possible if you set up OpenVPN server on the Diskstation NAS itself.
It's good to make sure your Diskstation NAS always has the same internal IP address. And if your ISP changes your public IP address frequently, you will need a DDNS server provider. (There are many recent threads concerning this.)
Your relative will also need to install OpenVPN on his/her laptop. As eliromer said, you will have to click the export button on the Asus VPN set up screen, to save the configuration file (normally this is called client.ovpn) on the user's Mac or PC. On a PC the configuration file should be saved here:
C:\Program Files\OpenVPN\config\client.ovpn
Because of Windows access rights, you may have to copy it first to a temporary location on the PC, then figure out a way to get it into the folder mentioned above.
It's important that both the OpenVPN server on the router, and the OpenVPN client on the laptop use the same settings. But if you export the config file from the router and save it on the laptop, this is done automatically.
There is a lot of information on the forum about the best settings for OpenVPN but the most important IMHO are to choose TUN (not TAP) and UDP (not TCP). These are I think the default settings in Merlin.
There are a lot of bad guys on the Internet who try to break into OpenVPN on routers, so you may want to make sure you use a non-standard adminstrator user name on the router (*not* admin) and a complicated password (16 characters max).
It's also good to change the port used away from the default 1194, but maybe this is a refinement you can do after you have got it all up and running.
If your relative is using a Windows PC to access the Diskstation NAS, he/she should map it in Windows using its internal IP address rather than its host name (for example, using \\192.168.x.y instead of \\DISKSTATION or similar). After starting OpenVPN and connecting remotely, the server drives can then be accessed in Windows Explorer exactly as at home. On the other hand, mapping in Windows using the server name (e.g. \\DISKSTATION) has not worked as smoothly for me.
I use this setup very frequently and it works fine. Speed is of course slower than when accessing the NAS from at home, because it is limited by the *upstream* speed of your Internet connection. But for light/medium usage, it's fine and much more convenient than carrying around paper.
As eliromer said, it's very stable and the OpenVPN connection stays up for days without any problem.