Indian clothing changed alot throughout its history. I am no expert, but will try to share what I know. Expect some massive generalization and North India focus.
Ancient Times ( Vedic ages to Islam invasion 11th century AD)
Characterized by absence of stitched clothing. People used to wear clothes which were tied together. Interestingly, sewing and stitching were known and very much in use for other purposes since Indus civilization. But it did not make inroad into clothing till Muslim age. Even a few decades back in rural India you would see men mostly wearing Dhoti, an unstitched piece of cloth in lower body. Women still wear Saree, which is unstitched.
Men would wear three pieces of cloth. Uttoriya on upper body, neebi as underwear and the dhoti ( I do not know what it was called back then) in lower body. For women, I believe they mostly would wear one or two long pieces.
Islamic age ( 11th century till late 19th)
Stitched clothes made inroads for males and for Muslim females. Purdah for women ( veils) was introduced in regular Indian family as well.
Modern age ( late 19th to current)
Males adopted western clothing, while women picked up the modern way of draping saree.
The modern way of draping Saree was invented by
Gyanadanandini Devi. She was wife of Satyendranath Tagore, first Indian ICS Officer and elder brother of R.N. Tagore, first Asian to win Nobel. After becoming an ICS officer, Satyendranath Tagore and his wife needed to socialize with English officers. The women of Tagore house did not want to adopt Western cloth totally, but the then prevalent way of wearing one-piece saree was not very civil for that Victorian age. Remember till then women used to stay inside their own home rarely seen by any male beside their immediate family, so the one piece saree was kind of adequate.
To suite with the new age, Gyanadanandini Devi started wearing Saree with Blouse, and semeez ( I am sure I misspelled that), which gradually became the Saree we all know now.