It's very common in instructions to omit the "sudo". sudo means "superuser do".
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You router in a home environment is assigned a private internet address group. The Internet can't find it because there are so many devices with the same IP numbers. The public IP address, from **broken link removed** gets assigned to you, temporarily by your ISP. The key here is it's temporary.
Your ISP also supplies two nameserver addresses; primary and backup. These translate names like gmail.com to addresses.
Your router, gets one of these private addresses, like 192.168.1.1; It becomes your gateway and you can point to it if you need a time server.
Your router may have 255.255.255.0 as a network mask, so everything on 192.168.1.x are accessible. .0 and .255 are reserved on this network.
Your router reserves some addresses as DHCP and some addresses as static. DHCP addresses have lease times. I usually use the longest lease possible.
Each IP address has a pool of ports attached to it. Ports below 1000 typically are used for well-known services. http is a service and it uses port 80 as default.
Every device has a MAC address permanently assigned to it at manufacturer. It usually can't be changed, but can in some cases. The MAC address MUST be unique across a routeable segment.
A Cable ISP uses this MAC address of your router to know it's you. If you replace your router, you generally need to cone the new router with the MAC address of your router provided by the cable company.
NAT or (Network Address Translation) does a lot of magic. When the Internet looks in, it can see one of the unique port numbers on only one of your computers on your private network. This is configurable in your router.
It also masquerades, your private IP address into the public IP adresss when reaching the Internet from within your public internet space.
Printers in general should have static IP address. So, should TV tuners, your router etc.
Windows has it's own browser and name server-like services. Some smart switches allow name server functions for TCP/IP.
ping -b 198.162.x.255 (subnet mask 255.255.255.0) pings the broadcast address. Most devices should respond, some don't.
arp -a will list the devices and MAC address that responded.