Our close friends have asked my husband and me to become the godparents of their children and we have agreed. I was wondering how we go about becoming the godparents through documentation.

Different denominations and/or faiths have their own customs and documentation procedures for this. It would help to know what faith and/or denomination in which this will be taking place in order to better answer your question.

A godparent is a person who stands with or for an infant at the time of their baptism. Legally to the state there is no documentation. Each denomination ( church) has its own rules as to who can be a godparent.
In ours for example you have to be a baptised christian to be a godparent. In some denominations you have to be a member of that specific denomination.

Normally the only documentation will be a copy of the baptism certificate. The godparents sometimes get a certificate showing they stood for the infant.

The only duties of a godparent would be to be sure the child is raised in the teachings and doctine of the church, esp in case the child's parents would die.

Thank you guys so much for the help