The router giving me trouble is a Belkin Wireless G
How exactly do I do that? There are a lot of other networks that come up.
Would this perhaps solve the problem of my iPhone saying "Safari could not connect to the server" (or what ever it says)?
It's under "Wireless > Channel and SSID" (in the router's web configuration pages).
It might help with the "not connecting to server", if there's another network that's on your channel, it could make it difficult to maintain a good connection. That, in turn, might affect the iPhone getting configuration data from the Belkin's DHCP server.
Usually, the symptom of being on the same channel is getting "bumped off" once in a while.
If you have a strong signal, but still have trouble connecting to the internet (server error), try entering your ISP's DNS IP address manually. You will see it in the Belkin's configuration Status page. On the iPhone, If you touch the right arrow for your network, you will see the configuration info. You can select and edit the IP for DNS. Of course, this is still assuming you are getting at least an IP address assigned [from the Belkin DHCP] for the iPhone ("IP Address" - should be 192.168.2.x).