Starting the case
In New York, a parent who is not in a divorce usually starts a custody case by filing a petition in Family Court, and the other parent must be served before the court can go far. When a divorce is pending or about to be filed, custody is generally decided inside that case in Supreme Court instead. If the child has recently lived in another state, the court first has to confirm it has authority to decide custody at all, under a uniform law that nearly every state shares. Filing does not by itself change the child's schedule, so many parents also ask for a temporary order at the first appearance.
How the case is built
Custody disputes are decided on the child's daily life, so useful evidence tends to be ordinary: school attendance and report cards, pediatric and dental records, a calendar of who handled pickups, and messages about scheduling. Keep your own communication with the other parent calm and in writing, because it may be read by a judge. Do not record conversations or post about the case online without first asking your lawyer. The court may appoint an attorney for the child and, in some cases, order a forensic evaluation, which can add time and cost. Courts also check for prior child protective reports and orders of protection involving either household.
Settlement runs alongside the litigation
Many custody lawsuits are resolved by agreement at some point, often after the evidence has started to come in and each parent sees the case more clearly. Some courts refer parents to mediation, though it is usually not appropriate where there has been domestic violence. In a first conversation we talk about the schedule you are proposing and why it serves your child, which facts may count against you, and what a temporary arrangement should look like while the case is pending. We also discuss cost and pace honestly, since a fully contested custody case can take a long time to reach a decision.