While you may have a specific dress style in mind, they were multiple types used in ancient Greece, and most were not specific to a particular gender. The 4 main types are the chiton, the peplos, the himation or the chlamys. None survived to this day, we only have sculptures, artwork and descriptions in ancient texts on how they looked like. Even tough we imagine them mostly white, the reality is that they were frequently quite colorful, and only truly white on some rare religious occasions.
As an example, this dress in the Athens 2004 Olympic Games is a good representation of the Chiton:
Types of ancient Greek clothing:
This unisex tunic was a common garment for day to day life, women wore it a little longer and men a little bit shorter, however, the principle was the same, one or two rectangular pieces of fabric stitched together on the longer side, and a belt was worn quite high. The chiton was the simplest form of attire at the time.
The Peplos is understood to be an earlier revision of the Chiton. It is made out of a singular long rectangular piece of fabric. Like the Chiton, it was pinned over the shoulders, however, unlike the Chiton, the cloth was folded twice at the top to give the illusion of a second layer of clothing.
The Himation was usually not worn by itself but on top of a Chiton or a Peplos. No pin was used to keep it in place but it was instead wrapped around the shoulder and the rest of the body.
Unlike the other tunics described earlier, this one was mainly geared at soldiers, and as such, essentially a male attire. Like most other garments of the time, it was also made of a single rectangular piece of cloth, pinned at the shoulder like the Chiton or Peplos. Being worn by men, it was quite short.
Modern day evolution:
The concept of wearing rectangular pieces of fabric wrapped around the body has been lost, however, the visual appearance has persisted and is still very popular nowadays. The main difference is that now, dresses are and worn mostly by women.
Even tough we have dresses of all shapes, sizes and colors, some of them retain those basic visual references that were already present in ancient Greece.