babysit
v.v. to look after children while their parents are away for a short time. You usually do this at the children's home and get paid for it.
v. to care for children in the temporary absence of their parents. Often used intransitively or with a direct object representing the children or the family.
I am going to babysit my neighbor's kids tonight.
She earned extra money during college by choosing to babysit for several families in her local neighborhood.
While the primary responsibility is to ensure the children's safety, many parents expect the person they hire to babysit to also assist with light housework or bedtime routines.
Back-formation from babysitter.
The verb is both transitive and intransitive.
I will babysit the children of my sisterI will babysit for my sisterWhen the object is the parent rather than the child, the preposition 'for' is required.