I need to know how to get paint to adhere to a plastic jug for a craft project for kids.

Paint will adhere to plastic that is slightly rough and porous, but not smooth and shiny.
You can rough it with sandpaper, but the results aren't usually very long lasting.
Painting plastic is often a problem.
I don't know of any product that acts as a base.

Try spray paint, there are a lot of colors and there is a specific brand can stick to plastics.