zajmować się dzieckiem in English:

They asked Kate to babysit their child.

I’ll ask my mother to babysit.

I babysit for Jane on Tuesday evenings while she goes to her yoga class.

What can go wrong when you're babysitting? (Co się może złego stać kiedy zajmujesz się dzieckiem?)

You can't babysit me 24 hours a day.

When I was little, grandpa and grandma would come to baby-sit. At night in bed grandma would read to me. Or grandpa would tell a story.