How do we see all the connections that a router currently has?
Is there a way to determine the IP addresses of the connected "users"?
If you have access to your modem you can use the modem configuration interface by entering 192.168.1.1 in your browser and then use admin for both and if your router's firmware is same as me (I forgot the name, the stock firmware in most routers) you can see list of connected devices with their MAC address:
Also to check for their Ip address you can use Advanced Port Scanner which is a free tool out there. Also try FING for android or ios which I think is better than Advanced Port Scanner.
OK, Just got back to see your model was posted. I linked to the manual at the bottom.
Before you get started, if you don't know how to get into your router, you would open a command box and type in
A lot of these home routers do not let you see if someone is connected with a wire, but that is probably not of real concern, but rather, you want to see who is connected wirelessly.
The following info assumes that you have an idea what IP addresses you actually have on your network, and anything else could be an intruder.
First, one clue as to who is connected would be anyone with a DHCP address. You can see that on page 7 of your manual. If someone has set their IP address statically, it will not show in this list.
Second, the most important indicator that someone will be piggy-backing your wireless will be the "Wireless Client list". This is on page 15 of your manual.
Lastly, you can look at the logs. This is found on page 24 of your manual. You need to enable this feature, and how to do that is also on that page.
Here is your manual:
First, input your default gateway IP into your browser. Then input your default username and password (or the default if you haven't changed it yet, which you should for security reasons.) Then you should get a log of all the devices on your network. If you see more devices than you know are using your network, someone is leeching. This way only gives you the MAC or physical address of the device, not the IP.