How can people living under repressive regimes communicate safely?
Running your computer output direct to your modem will result in your identity being observable to anybody who checks.
Activating VPN on your computer can establish a connection with a VPN repeater somewhere else in the world, which then puts out your signal with an identity consistent with originating at that remote location. So somebody in Dublin can set his/her VPN to Hong Kong and thereafter communications appear to come from some address in HK.
If you are given access to someone else's Router, e.g., in a hospital or a cafe, your communications will go out through the other party's modem. I haven't tried this, but it should be possible to activate your VPN and have your Internet activity appear to originate in some remote location.
You can use something like a TOR browser to go directly to a TOR connection with the outside world, or you can use your VPN to go to a TOR connection. The most highly regarded VPN service, ExpressVPN, is in favor of communicating this way if you are in a bad situation.
Evauations of VPN services for Afghanistan.