By demanding the same equity in court that women have been demanding for half a century. Unless a court wants to baldly declare that women are inherently the better gender for parenting -- as archaic a notion as any I've heard lately -- then they have to parse maintenance responsibilities and custodial rights equally.
There are concerned mens' groups who are starting to advocate for men's rights in divorce settlements. FOr example, the American Coalition for Fathers & Children (www.acfc.org). Start there.