Steps to better performance

I have an AT&T FIOS Phone/WiFi router that stinks.

I have a faster WiFi router I want to use to replace the AT&T for the
wifi and router parts.

How do I do this ?

Basics I think are to:
somehow keep the AT&T unit so phone will work but not use it as a
router or a WiFi.

connect new wifi router to AT&T with a cable.

I can get into the AT&T unit and print the settings but I do not know
what settings are important.

What things do I need to do to make it all play and not have to change
all the passwords on my equipment.

Please give me steps in order with as much detail possible

Thank you so much.