The pattern uses the Tunisian reverse stitch (R).
The larger size hook is the Tunisian hook for making the dishcloth, the smaller hook is for edging the finished dishcloth.
Two colours of cotton are needed and the patterns states Coats or cotton worsted yarn:
100yds / 73m #1021 Linen (CC)
40yds / 91m #661 Frosty Green (MC)
All the patterns in this book were designed not to curl.