I (Rhi) have been embroidering since I was a kid, and when I joined the Society it seemed very natural to use my embroidery to decorate my garb. My very first SCA embroidery project was some fairly involved celtic knotwork around the cuffs of a cotton/poly t-tunic. By the time I had finished the embroidery, I had been around long enough to realize how bad the garb was and I promptly donated it to loaner gear! Further projects have improved incrementally. My skill at embroidery far outstrips my knowledge of embroidery history and documentable pieces/stitches; suggestions are welcome!
Embroidery of some form pre-dates the Society period – in other words, there some form of embroidery that’s appropriate for almost every persona! A large portion of extant medieval embroidery comes to us in the form of liturgical garments and hangings, which are often incredibly ornate – beautiful, but impractical to duplicate for Society clothing. Personally, I often take inspiration for embroidery motifs from illuminations, mosaics, and other period artforms.
Specific stitch techniques that are documentable to period include split stitch, stem stitch, couching, chain stitch, and satin stitch. If you want to learn specific stitches, there are many modern embroidery books available.