Nice question . Well one of my theory is that fox took care of him (Becouse it's not nice if your host dies ). My second theory is that there is some sort of orphanage in konoha . I really dont see any other way
I believe the third took care of him,in his infant days and when he was of age he go his own apartment and when he became a ninja he survived off his mission salary.
<div class="bbWrapper">I guess that the 3rd hokage kep him undr his guidance until he was 4 or 5 and then left him to live his own life in his own way</div>