I started with a base coat of Julep Donna, a deep teal color creme. It matched the blueish colored rug in the opening scene of the show.
After layering the white I went over with the largest colors used in each character. The rugrats were skintone, hair and shirt color, spike was brown for fur and the logo was a light purple. I went through and added my black outlines then filled in the little details and colors there. In a few places I had to go back through and touch up any little error or out of place colors.
And voila! Only two and a half hours and I'm done.
I finished up with Butter Londons Matte Top Coat to make the design look more 2-D and cartoon-y.