States generally use one of two standards for determining custody. The courts in many states currently begin any proceedings by looking for the parental preference, meaning that the wishes of the child’s parents will be followed unless there is strongly significant evidence to the court that they should not be respected.
The reason for this is that the constitution gives a fit parent the right to determine what is best for the well-being of their child. Generally a grandparent then has the responsibility in overcoming parental preference by proving the parents are (to a great degree) unfit to have custody of their own children before the court will consider the grandparents for custody.
States without a disposition toward parental preference generally try to follow the best interest of the child as the decisive factor in granting custody. Although this is not as difficult a standard for grandparents to overcome as parental preference it still means that you may have to prove why a parent is largely unfit to have custody while supporting your own claim.
In my book No Greater Loss I discuss the fact that in the Troxel v. Granville case, however, the Supreme Court made it clear that the best interest of the child should not be the sole reason (or only factor) for granting custody. This becomes an important factor in many custody cases.