Q: How do i set up a new apple account for my second phone

You have the choice getting another account then adding both to the family plan or leaving the accounts separate.

settings > itunes & app store > apple id > sign out.

Next time you come back to settings and go through this tapping, you can make a new account.

You will want to go through this path to setup you icloud backup.

http://www.apple.com/icloud/family-sharing/

Set up Family Sharing - Apple Support