Ok lets reitterate -
Your router has two networks attached to it. One is the network connecting you to your ISP and has a public ip address. i.e. one that is recognised by any host on the internet.
The other connects to your LAN which is using the network 192.168.0.x. This is a network in the reserved range of 192.168.0.0 to 192.168.255.255. Any networks in this range do nt exist as far as the internet is concerned. This allows you to use these addresses in your private network and still connect out to internet hosts without fear of address conflicts.
Now obviously for outgoing connections from your PC to the internet, the internet must perceive them as coming from your public address not your private one, or return packets will never get to you. Remember 192.168.0.x doesn't exist on the internet.
This function of pretending that your outgoing connection is comming from your public address is called Network Address Translation or NAT and is performed on on the router. All outgoing packets are edited to show the public address as source. All incomming packets are edited to show the private address as destination.
To make configuring your LAN easier your router is acting as a DHCP server. This allows your PC's to dynamically configure themselves with address info from the server when they boot up. The router will probably be handing out addresses in the range .100 to .254 or something like that. If you want to fix your PC's IP address you need to disable DHCP on the PC and manually configure an address into it. If you pick something in the .50 to .99 range you won't risk any conflict with a DHCP configured device
Another peice of info that your dhcp server will be handing out is a DNS server or nameserver. DNS is the system by which your PC converts names into IP addresses for you, allowing you to type
www.google.com and actually connecting to 219.132.6.45 or whatever.
If you switch DHCP off then your PC's will no longer learn the nameservers to use at bootup from the DHCP server. So like the IP address this needs to be manually configured on the PC and resolv.conf is where this information is kept.
How exactly you configure IP addresses and nameservers is dependant on your distribution. If it has configuration tools, like Suse's YaST then use them. If not you will need to edit config files with vi or something.