There's a few ways you can find out this information:
Look on the top, sides, or bottom of your router for the manufacturer name and model. In the example below, looking at the top and bottom reveals that the router is a Linksys EA9500 V2. Linksys is the manufacturer, while EA9500 V2 is the model.
If it's still not clear, you can search the Internet using identifying items on the router, like the label or name.
You can also talk with your Internet Service Provider to identify your router.
Once you find your router model, check to see if it's compatible with the Bark Home device here.