Legal aid defends people for all sorts of legal issues. They do not have to be accused of a crime. The legal aid office is staffed with lawyers that work in that office.
A court appointed attorney is chosen from a pool of regular practicing attorneys that have requested to be put on the list They make a set sum per hour, that is paid through the court system.
Many attorneys want to be on the list to be court appointed. It is guaranteed income. The are still free to take on cases from people that have walked in off the street and need their services too.
Legal visitation with his child requires him filing for joint custody (I am assuming he's not trying to take the child from the mother, so he's not looking for sole custody, and there is no legal custody agreement currently in effect). HOWEVER, when he does that, child support will be brought up and he will begin paying it. Be warned that if the situation with the mother is acrimonious, she can ask for back child support from the day the child was born.
Now, to answer your question, he needs to contact his local court (I am assuming he lives in the same jurisdiction as the mother and the child), go to the family division, talk to the clerk, tell the clerk what he wants to do and the clerk will give him the necessary documents with instruction.