Can I connect two networks, one wired, one wireless, so that I can access the Internet through the s
I assume that your wired network router is using NAT, providing all eight wired stations with Internet access through the router's WAN IP address. If you disconnect that router's WAN port from its cable modem and reconnect the WAN port to a LAN switch port on your wireless router, it will obtain a new "WAN IP" from the wireless LAN subnet and route traffic through the wireless router and its cable modem to the Internet.
If your wireless router doesn't have an available Ethernet port (most wireless routers do), you could connect your wired router's WAN port to a wireless bridge. But you may not want to do that for performance/reliability reasons.
The reason I did not suggest connecting your wireless router's WAN port to an Ethernet port on your wired network router is to keep your wired domain completely isolated from your wireless devices. It is quite likely that your wireless router would (by default) block any NetBIOS traffic from passing between the two subnets, but it is safer to bring wireless traffic into your network OUTSIDE your wired network's firewall.
One last note: Your wired network router's LAN and WAN IPs must be from different subnets. If both routers happen to now use the same LAN subnet, you'll need to renumber one before connecting them as described above. For example, if both routers now use 192.168.1.0/24, reconfigure your wireless router's LAN to use 192.168.0.0/24 instead.