To make the handprint leprechaun:
Paint the fingers orange to create a beard. Then use a peach color to paint half the palm - this will be the face. Next, paint a strip of orange hair on top of the peach color. Use green to paint the rest of the palm and thumb creating a hat. Now you're ready to press it onto the paper! It would also look good having the fingers closed instead of open to make it resemble a beard even more.
To make the rainbow:
Use your fingers instead of a brush to paint the colors of the rainbow. Dip the pointer finger blue or white paint. Dab a bunch of dots on each end of the rainbow to create clouds.