If you want to make authentic archaic age (early) Greek costumes, the hardest part will be getting the rectangles of wool (all white is a good choice) to make the Dorian Chiton or tunic. The accompanying diagram from the British Museum shows how and provides directions. You take a rectangle of cloth about twice the span of your arms and a bit taller than you, fold it down at the top so the flap will fall somewhere around your waist when the fold is at your shoulders and the bottom at the ankles. Then you fold it in half so there is a vertical "seam" (really the fold) on one side and an open edge on the other, Before going further, the top front and back need to be attached with long straight pins (preferably gold) facing front, at either side of your neck.
My own experiments -- albeit with considerably lighter weight fabric -- show that, if you're doing it alone, it is best to make a guess as to where the pin on the closed side should go while the fabric is off your body and pin it, even if temporarily; then stick your arm through the arm hole so generated. This arm hole should be on the side of your dominant arm, so you can reach over to pin the other side. This will result in the reverse of what is shown in the picture if you, like me, are right-dominant, but you can pull the chiton off just far enough to turn it back to back after you've finished pinning if (1) you leave enough neck/head room, and (2) you use safety pins rather than forward-facing straight pins.Now the rectangle will stay on your body, but you will be exposed, because one side of you has fabric that gapes. In the diagram, the gape is on the figure's right side. The solution is to wear a "girdle" or belt of some sort along your waist.
Pins facing your cheeks are an accident waiting to happen, so they should be replaced with safety pins or brooches*. Today's notion of modesty probably requires sewing rather than simply belting the open side, but don't worry: it's not anachronistic. Sewing the side was an option.
* Buttons are a possibility although you should do further research into their construction and the mechanism for using them. See: "Buttons and Their Use on Greek Garments," by Kate McK. Elderkin; American Journal of Archaeology (Jul. - Sep., 1928), pp. 333-345.
Also note this article on specialized clothing for Greek women: Heraia Costume