Are the two networks within the same building/home? If so, you could use a router between the two and add a static route to your computers to direct that particular subnet across the router instead of going to the Internet. If they are not physically co-located, the only way to make them see each other is setting up a VPN (virtual private network) across the Internet. Much more complicated.
Right now, your routing tables are telling your computers that anything not on their particular subnet (i.e. 192.168.0.x) must go to the Internet. Adding a static route will tell your computers that 192.168.10.x is available without going to the Internet, and directs the traffic to the router you assign to the path.
If you don't understand IP routing, don't feel bad, most non-IT support people don't (and even some of them are confused

). what you can't do is just plug both subnets into the same network switch.
I have created both types of inter-connections (VPN and router) and once they're set up there's usually not much else required. However, setting it all up if they are not close to each other is a little tedious, going between the sites to configure and test everything can get time consuming depending on how far apart.
Dan
LG NANO85 4K TV, Samsung JU7100 4K TV, Sony BDP-S3500, Sharp 4K Roku TV, Insignia Roku TV, Roku Ultra, Premiere and Stick, Nvidia Shield, Yamaha RX-V583 AVR.
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