Judging by portraits in the decade, a sari style like a warp was quite popular in the 1930s. It appears to be wound once so the sari border crosses or falls around the knee and then wound again to drape the sari over the shoulder as per usual.  Often teamed with a sleeveless or cap sleeve or “mega” sleeve blouse which were popular in the decade (and a change from the long sleeves of the previous decade). Of the 1930s examples, girl in blue sari painting by  Hemen Majumdar.  Other examples: Amrita Shergil and Lady Andal.

Another example of the sari style is found in Raoul Dufy‘s 1930 painting of Interior with Indian Woman. Again the sari is wound twice, the blouse has just the hint of a sleeve (if at all).  Here the sari is pinned to the shoulder and then draped over the head.  Also common in 1930 though the style was in its way out over the decade.

It appears that the pleats are formed first and the the sari tightly wound in the manner required.

An adaptation of this style can be seen in the 1960s and was wildly popular once worn by Mumtaz.  This style, seen here on Mumtaz in a 1968 film, is far more stitched and structured. Indeed Bhanu Athaiya, the designer, practically stitched her into it. As in the 30s, sleeveless blouses were popular in the 60s.

The modern take is of Priyanka Chopra channeling the “saree wrap” look (also see Sonam). Though idk, no one can top Mumu:). The link provides a bit of info on how the style should be worn: keep the “pallu” long and narrow, wrap as many times as required around the waist and then drape over shoulder.