ip inside your network can be 10.0.0.4 or 192.168.0.4 .
Now you can set default route toyour gateway (router)
But you must get router ip first. Fortunately you set your interface ip and this is where your network address comes from (ip masked by netmask). To get your router ip requires change the address end .4 to some common number like 1 or 138 or 254. The router ip and client ip must belong to the same network to get ping functional.
So try: ping 10.0.0.1 first when you set your ip 10.0.0.4, etc.
If you can ping your router then set the default route:
sudo route default add gw <yourrouterip> eth0
Cool you can check your default route with the route command.
The last step is set your dns server. But check your default route before, just try ping some ip outside your network, like google dns server 220.127.116.11 .