Where in the Quran does it say to wear hijab?

Surah an-Nur (24:31)

This is the main verse. It tells believing women to lower their gaze, guard their modesty, not display their adornments except what normally appears, and to draw their veils over their chests. The men are told first to lower their gaze and guard their chastity too (Quran 24:30).

The khimar was an ordinary head covering that women already wore. The verse tells them to bring it down over the neck and chest. Aisha said that when this verse was revealed, the women of Madinah tore their wrappers and used the pieces to veil themselves (Sahih al-Bukhari 4758). See Does my hijab have to cover my chest?

Surah al-Ahzab (33:59)

The verse adds that this makes them more easily recognised as respectable women and protects them from harassment. A jilbab is a loose outer garment, so this verse points to modest, loose clothing in public.

How scholars understand these verses

• Most scholars, from all four schools (Hanafi, Maliki, Shafi'i and Hanbali), say these verses make covering the hair and body obligatory in front of men who are not close relatives.
• Face and hands: scholars differ on "what normally appears". Many say it means the face and hands; others say the face should be covered too.
• Some modern writers argue the verses call for modesty without fixing a head covering, but this isn't the view of the classical schools.

For a clear overview, see Is hijab mandatory in Islam?

For new Muslim women

Many new Muslims take this step gradually, and that's understandable. If you're unsure where to begin, a trusted local imam or scholar can advise you for your situation. The Quran also reminds us that "the best clothing is righteousness" (Quran 7:26).