Its a bit complicated and depends on your ISPs support level.

If your ISP supports basic IPv6 they will likely use SLAAC or DHCPv6 to advertise the /64 that any directly connected devices, like your router, can use (/64 being the default size for a single LAN segment, even between point-to-point connections). If you have devices behind that router that want to use IPv6, you will need additional prefixes. The most common method nowadays is to use Prefix Delegation (DHCPv6-PD) where your router will ask the upstream router for an additional routeable prefix which you will use on another interface of the router. The RFC for prefix delegation recommends a /48, but many ISPs are not delegating that much. I only get half of a /60 from my ISP's modem.

If the ISP just provides you a static routeable prefix, then you would just assign that to your router's interface and enable SLAAC/DHCPv6 to give out that prefix. This would only need to be configured in a single device and is why they don't recommend hard coding servers and workstations with IPV6 addresses.

Keep in mind that your router will also need a firewall as all of these IPv6 prefixes are routeable and public. While IPV6 space is quite like finding a needle in a haystack, you could still find yourself having a bad day if you treat it like private IPV4 space.

The end result though is that you would setup DNS so that devices register their IPv6 addresses and it just works. There's also the MDNS protocol that supports IPv6 which will do segment-local resolution for device names.