When an Account Request is approved, the card is changed into a User card. If you want some of the sign-up (account request) fields to show up on the eventual User card, just include the same card on the User card using structure.
Note: both the Sign up and User types may be renamed -- they'll still work.
You can use structure on the relative inclusions to determine their type. For example, if you're including +birthday, then setting the Cardtype of birthday+*right+*default to Date will make it so that they're presented with a date picker rather than a text box to enter their birthday.
You don't have to put all of the nesting from Sign up cards into User cards; they'll still be in the system.
Note that this information will not be requested when someone is invited to a Wagn by way of the "Invite a Friend" link.