Connecting the router
O.K. Now that we have collected all information which may be helpful it is time to connect to the router. Please always do the initial configuration of a router with a wired connection. Although it is possible in theory to configure the router completely from a wireless computer it is highly advisable not to do so simply because otherwise you'll never know if it is really your wireless router which you configure or your neighbor's.
Thus, use a ethernet cable for the initial configuration! O.K. Set up the router. Plug in the power cord and connect it to power. Do not connect anything else yet to the router. Wait until the router booted up and the lights stop flashing/blinking or whatever they do during booting. Now wire a computer to one of the LAN ports on the router. If possible, use the computer which you have used before to connect to the internet directly through the modem. Again do not connect the router yet to the modem. All you want at this moment is a wired connection from the router to the computer.
Now run "ipconfig /all" again. This now shows the settings on your computer when connected to the router. This time all information should be in the local area connection. The default gateway IP address and the dhcp server ip address should be identical. It is the IP address of your router. Please write it down. You'll need it in a second. For Linksys routers this is usually 192.168.1.1. For Netgear it is usually 192.168.0.1. Take a note of the subnet mask, too. You should also find this default IP address of the router in the documentation which came with the router.
Avoiding address conflicts
This only applies if you had two different IP addresses in the modem check before: you have to make sure that your router which you configure now does not create an ip address/subnet conflict with the modem or whatever router there is on your path to the internet. This requires some math. But most of the time the situation is very simple. Anyway, what you have to make sure is that the IP subnet used when the computer was not connected to your new router does not overlap with the IP subnet used in the LAN of your new router. If it overlaps the router cannot work properly.
In most cases the subnet mask is 255.255.255.0 which makes this much easier to find out: if you found with "ipconfig /all" above that your router has IP address 192.168.1.1 and subnet mask 255.255.255.0 then all IP addresses 192.168.1.* belong to the LAN IP subnet. With subnet mask 255.255.255.0 the first three numbers are fixed and only the fourth number can vary.
Now, you will have a problem if your new router uses the same IP subnet as the modem/router to which you will connect it. Again, if you found the subnet mask 255.255.255.0 before in the modem check in part 1 it is simple. You have a conflict if the IP address found in the modem check in part 1 uses the same first three numbers as you just found connected to your new router. For instance if you found that your computer had an IP address of 192.168.1.123 with subnet mask 255.255.255.0 when it was directly connected to the modem and now you find that your computer has an IP address of 192.168.1.100 with subnet mask 255.255.255.0 when connected to the router this means you will have an IP address/subnet conflict if you connected the modem and the router without any further changes.
To fix this problem the easiest way is to change the default IP address of your new router. If you move the IP address of your new router outside the IP subnet used by your modem then you have resolved the conflict. Again, with subnet mask 255.255.255.0 this is fairly simple by changing the third number of the ip address. For instance, change the IP address of your new router from 192.168.1.1 to 192.168.2.1. Please remain inside 192.168.*.* as those addresses are for private use. We'll change the LAN IP address in a moment...
Accessing the router web configuration interface
Now it is time to make changes to the router settings. For this you have to connect to the web interface of the router. You open a browser and enter the IP address of your router which you have written down before. For instance, for a Linksys router you should have found 192.168.1.1 above and thus you enter 192.168.1.1 or http://192.168.1.1/ if you like into your browser.
I would recommend to have a look in the manual to find out how exactly you connect to the web interface of your router and in particular what the default username and password is to connect to it. With some routers like Netgear's you don't have to enter the IP address but you can also enter the URL http://www.routerlogin.net or similar instead. That makes it sometimes easier.
Moreover, you'll need the default username and password for your router. For Linksys you usually don't have to enter any username. The default password is "admin". For Netgear the default is usually username "admin" and password "password". But please check the documentation of your router (which either came in the box, is maybe on the CD or available for download from the web site of the router manufacturer).
For the initial setup you'll have to find where you do the basic settings for the WAN and LAN. On Linksys routers you usually find all this on the very first setup page you'll see when you connect to the web interface. Other routers show a status page instead and you have to select some category like basic settings, WAN settings, LAN settings or similar. Again, the documentation may help you to find your way around.
Change the LAN IP address of the router
Now that you have managed to get into the web interface of your router you can start with the initial configuration. The router is still not connected to the modem! If you have found before that you have an IP address/subnet conflict and you have to change the LAN IP address of your router this should be the first thing to do. If you did not found a conflict or the modem check showed a direct connection to the internet you can skip this step.
Find the LAN settings of your router. Find where the IP address of the router is set at the moment. You know the IP address which you have found above thus you know what you are looking for. For Linksys it is usually somewhere in the middle of the first setup page. The address you have found was probably 192.168.1.1 and that is the address you should see there at the moment. Change the address to something else, e.g. 192.168.2.1. Save the changes on this page. The router will now reboot and you'll loose the connection. That's O.K.
After the router resumes normal operation try to connect to the new IP address of your router, e.g. http://192.168.2.1/ If it does not work, unplug the ethernet cable for 30 seconds, then plug it back in, or reboot the computer. Your computer needs a new IP address from the router inside the new IP subnet 192.168.2.*. Once the computer got the new IP address from the router you should be able to connect to the web interface on the new IP address. Please write down the new IP address for reference. If you router does not use a nice URL like Netgear with www.routerlogin.net you'll need the new IP address in the future and in particular for all following steps.
O.K. With this change the router is prepped to be connected to the modem now. That was a lot of preparation but the remaining steps should be much easier now...