Actually just an ethernet cable (Cat5 or better).
ADSL (via ISP) will come in and go to a splitter (sometimes referred to as a filter) and the one incoming wire will be divided (via the splitter/filter) between a modem and a telephone. The modem would provide a single ethernet port from which to run a cable to the router's WAN port. (But some ISP's may provide a combination modem/router. You would just configure that ISP provided device as a passthrough and configure your own Archer router do the network functions.)
Likewise for Coax.
However if your location already has a router you may attach your router to permit more devices to connect. You will need to "coordinate" the routers - i.e., IP addressing, subnet masking. The existing router being responsible for IP addresses etc., and your router just becoming a switch or hub. That connection will most likely be via LAN port to LAN port. An ethernet cable will still be used.
The devices (make and models) become important with respect to any specific connectivity.