How to use house's built in patch panel
So, based on what I can see there, that's not an ethernet patch panel.  The cabling is CAT5, which can be used for ethernet, but those are all being used for phone lines.  It looks like there's also a coax splitter, and some unused CAT5 cable.  

In general, if you wanted to, you could probably repurpose that CAT5 cable and use it for ethernet, but you'd need to get an ethernet switch or hub, and find a way to get the router to connect to that switch or hub.  You'd also need to turn some/all of your phone jacks into ethernet ports. And hope that the builder didn't do something that would preclude using the CAT5 cable for ethernet.  Depending on where the line from the ISP comes in, that could be easy or hard.  

Optionally, you might be able to use those  existing CAT5 runs to pull more cabling, but again, that would depend on how the contractor ran the CAT5 cable (ie, conduit vs staples).

For much more information, I'd suggest reading through https://www.structuredhomewiring.com.