How to prove a parent is un fit

You'll have to present evidence as to why they are a bad parent? Perhaps pictures of abuse, testimony from the child, etc.

Child Custody Guidelines.
Montana laws use guidelines to determine custody in accordance with the best interest of the child. The court shall consider all relevant factors, which may include but are not limited to:

(a) the wishes of the child's parent or parents;

(b) the wishes of the child;

(c) the interaction and interrelationship of the child with the child's parent or parents;

(d) the child's adjustment to home, school, and community;

(e) the mental and physical health of all individuals involved;

(f) physical abuse or threat of physical abuse;

(g) continuity and stability of care;

(h) developmental needs of the child;

(I) whether a parent has knowingly failed to pay birth-related costs that the parent is able to pay, which is considered to be not in the child's best interests;

(j) whether a parent has knowingly failed to financially support a child that the parent is able to support, which is considered to be not in the child's best interests;

(k) whether the child has frequent and continuing contact with both parents, which is considered to be in the child's best interests unless the court determines, after a hearing, that contact with a parent would be detrimental to the child's best interests. In making that determination, the court shall consider evidence of physical abuse or threat of physical abuse by one parent against the child.

(l) adverse effects on the child resulting from continuous and vexatious parenting plan amendment actions.

-From 40-4-212 of the Montana Code.

This is from some of my own research, and from what I can tell this is just about the same for every state. But if you can prove that this person is in some way a danger to this child or that it would be in his/her best interests to be removed than this is the only way to do this.
P.S unfitness is in a lot of ways a mater of opinion of the judge.

And at the end of the court day it will be what your local judge believes is unfit and to the best interst of the child.
As I have told on here several times over the year.
We have a businessman remarried, in large home, fensed yard and a great father of his step child. We had his ex, proven a hooker in court, lived in a trailer next to a XXX movie place, she left younger chlidren to be watched by a 9 year old, who had to cook and watch his younger brother and 1/2 brother and 1/2 sister. Photos from inside the home showed, trash and trash bags everywhere, it showed beer bottles everywhere in the home. They had proof of a list of various men she even brought home and sleep with for money with the kids in the other room. Even had proof of drug use.
Allof the evidence was allowed and accepted by the court.

Guess what the man lost, the women still keep custody, the local judge just would not give custody away from the mother.

Even a few years latter, when social serivers removed the child for what it considered serious child abuse, they still gave the children back to her after a parenting class.

So at the end of the day, you will need all of the evidence you can get, but it will end up in what the judge will or will not do.