Most modern computers have a built-in network adapter (typically located near the top right above 2 USB ports), Windows 10 should have the device installed already.
The cable that comes from your modem to your wireless router will also plug directly into that port. It's a typical RJ45 port which is usually Cat5 or Cat5e. If you have your computer setup for DHCP (automatic IP address), it should connect automatically to the Internet through the modem. Some ISPs, though, require PPPoE authentication, so you'd have to check with your Internet Provider to see if there are any special configurations that need to be done (most often not).
Keep in mind, though, that this isn't the most optimal way. Your wifi router would have a firewall built into it to prevent attacks. Windows 10 also does have a firewall built in, but it's not entirely perfect. The firewall on the router would add an extra layer of protection from the outside world. Most wifi routers also have multiple ethernet ports built into them so you can hardwire devices directly into them (such as a desktop PC). You can pick up Cat5/Cat5e ethernet cables from any electronics store fairly cheap (about $0.50/foot).