My router is a full on Linux server PC in a rack, so in my case I can just monitor all its interfaces directly on the box. I've got an entirely seperate VLAN for my IoT stuff (because a LOT of them are still very unsecure and I'm more scared of my network being compromised that way, by them just getting straight up hacked).
An easy way to do it in your case if you have a gimped ISP-provided router is to find an old hub (not a switch), plug a wireless access point into that, and have the device connect only to that access point. Then plug your laptop or computer into one of the other hub ports and you should be able to listen in on everything being sent across that hub.
More advanced switches might be able to do port-mirroring, which accomplishes the same thing.