Assuming that the Ethernet wall ports have been correctly wired, the port in each room will be wired back individually to a patch panel possibly in a cupboard, utility room or in the basement. If there is no patch panel, and the ports are all connected in a chain, then they are incorrectly installed and will not work reliably.
The next thing to find out where the Internet connection comes into the building. If this is in the location with the patch panel, then you will have to install the modem (connected to the incoming cable) and a router by the patch panel. (In some cases, the modem might be integrated into the router without a separate box.) Assuming that the router has four PC/LAN Ethernet ports (most home routers do), connect three of those ports to three ports on the patch panel. These should be the ports for the rooms that will have the most traffic. Then you need an Ethernet switch (not a hub) with at least one more port than you have remaining rooms on the patch panel. Connect the remaining ports on the patch panel to the switch, and also connect the last port on the router to the switch. If you want WiFi in a specific room but no Ethernet, then you can use a wireless access point (WAP) connected to that room's wall port (assuming the WiFi from another room is not strong enough). If you want WiFi and Ethernet, then you will need a switch and a WAP in that room. The switch connects to the wall port and the WAP, and Ethernet devices also connect to the switch.
If the Internet comes in elsewhere, then you have to install the modem and router there, and connect one of the router PC/LAN ports to the wall port. At the patch panel, you will need a switch connecting to all the ports on the panel including the one from the router.
If you have multiple WiFi sources (the router and WAPs), make sure they use different channel numbers at least 4 channels apart. You can use the same network name (SSID) and pass phrase on each, but personally, I find it more reliable to use different network names unless you want to walk around the building while actually using a WiFi connection.
Games consoles will almost always work better online using Ethernet rather than WiFi.
I hope this helps.