There are many ways to store your embroidery floss, but here's my favorite. I have a lot of skeins that I use during workshops, so I need to unpack them and pack them in a way that keeps the colours together. If you knit you've probably already recognise the stitchholder i'm using. It was an epiphany when I finally realized I could use them to organize my embroidery floss. I can store 12 skeins on one pin and then stack all the skeins into a clear box where they sort of hold themselves up.
These are 13,5cm stitchholders from prym. You can find these and many others on Amazon (affiliate link)