There should be nothing to it.  The linksys router will be acting as the DNS server on your network.  This will allow any computer you connect to the router via a network cable to get an IP address.  Assuming that you have a cable or other high speed access, the correct thing to do would be to get every thing set up first then power on the devices one at a time.  What type of setup are you planning on going with?  Other factors include;  Is the router already set-up and working , or do you currently just plug your computer into the modem?  The type of modem (i.e. Cable DSL) matters as well.  The company that provides the service dictates how the router will need to be setup.  Can you provide a little more info on your current setup and the target setup?

 

Jim