You will have to identify the new router with by SSID and password to all the wifi connected devices in your home.
It's easiest (and more secure) in the long run to log into the new router and create your own SSID and password. But I've noticed a lot of people just use the SSID and password that is printed on the back of the router.
Most annoying part might be discovering how many wifi-connected devices you have in your home and trying to remember how to reset the wifi on each of them.
Does that help? Chances are the new router will come with some setup instructions, or you will have a support number to call for step by step instructions.