Before you begin, learn the basics of embroidery.
Armed with these basics, you can create charming personalized handkerchiefs. Since the designs are small, it's a good project for a new embroiderer. Practically any image can be stitched. Buy an iron-on transfer from a crafts store, or trace an image from a book (with permission) onto transfer paper with a heat-transfer pencil. Iron directly onto fabric.
Depending on the stitch, monograms can look tailored or soft. A child will like a Scottie dog embroidered in satin stitch and stem stitch. Give a businessman or woman a paper-clip handkerchief, stem-stitched in metallic silver thread.