Islam doesn't tell you exactly and explicitly what to wear; however, it talks about maintaining modesty and the awrah
. This is the part of the body which must be covered.
For men, the awrah is from the navel (belly button) to around the knees.
For women, it's a bit more complicated, but around unrelated men, they should cover their full body and observe the hijab
. Nowadays the word hijab is thrown around without understanding the actual meaning. Hijab is not a piece of cloth, it's a way of life. It means to remain modest, to lower your gaze and to guard your private parts.
Allah says in the Qur'an: "And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts, etc.) and not to show off their adornment except only that which is apparent" 24:31
Modesty can be achieved by wearing long, loose clothing that covers the upper and lower body, as well as a headscarf that covers the neck and the hair. If a woman wants to observe the hijab further than this by wearing a burqa or niqab, they have the free will to do so if they feel closer to Allah.
On occasions such as Eid or Jumu'ah, clean, new clothing should be worn especially when going to the masjid.
O children of Adam, take your adornment at every masjid, and eat and drink, but be not excessive. 7:31