To make a mermaid tail for kids, trace the outline of the child onto paper, flaring the lower legs to form a fin. Use this as a pattern on folded Lycra. Sew the pieces together, form a casing for the waist, insert an elastic, and sew the ends together.
Instructables.com gives step-by-step instructions on how to make a mermaid tail suitable for swimming. First, swimsuit material long enough to wrap around the child's body is folded in half. A monofin that fits both feet into a single fin can be purchased at FunFinMermaid.com. The monofin can be used as a template to trace around the fabric that forms the mermaid tail. Add 1 inch of seam allowance to the paper pattern for a child. After cutting out the fabric, pin the fabric pieces right sides together, and sew around the perimeter. Finish the waistband, and insert the fin.
To make a no-sew mermaid fin costume that is not meant for swimming, take sparkly blue fabric and cut a rectangle with a fin shape at the hem. Small pieces of Velcro can be added to the top of the rectangle to form the waistband. The rectangle becomes a wraparound skirt. Images and instructions for this tail can be found at LivingLocurto.com.