I have a brother whom has a background but he wants full custody of his child. What all do he need to do?

Your brother needs to consult with a family law attorney to get information on petitioning for custody. There are low cost legal aid clinics in most states, and your state's bar association is a great place to start.

As far as his background, if he has changed his life around, letters of reference to show such positive changes coupled with a stable job and home environment will go long way in furthering the case of being a stable parent.

In any case, he needs specific legal advice only an attorney can give based on the specifics of his case. Good luck.

Custody is awarded by a Family Court. Such courts are charged with acting in the best interests of the child. If the court thinks its in the best interests of the child for the father to have custody they will award it.

Having a "background" may bring his fitness into question.

As solamente said, a consultation with an attorney will give him a much better idea of his chances.