Source of Rulings on Islamic Dress:

Islam gives guidance about all aspects of life, including matters of public decency. Islam has no fixed standard as to the style of dress or type of clothing that Muslims must wear. However, some minimum requirements must be met.

Islam has two sources for guidance and rulings: 

the Quran which is considered to be the revealed word of Allah, and the Hadith or traditions of the Prophet Muhammad, who serves as a human role model and guide.
1st Requirement: What parts of the body are to be covered:
The first bit of guidance given in Islam describes the parts of the body which must be covered in public.

For women: 

In general, standards of modesty call for a woman to cover her body, particularly her chest. The Quran calls for women to "draw their head-coverings over their chests" (24:30-31), and the Prophet Muhammad instructed believing women to cover their bodies except for their face and hands. Most Muslims interpret this to require headcoverings for women. Some Muslim women cover the entire body, including the face and/or hands.

For men: 

The minimum amount to be covered is between the navel and the knee.
2nd Requirement: Looseness:
Islam also guides that clothing must be loose enough so as not to outline or distinguish the shape of the body. Skin-tight, body-hugging clothes are out, for both men and women. When in public, some women wear a cloak over their personal clothing as a convenient way to hide the curves of the body. In many predominantly Muslim countries, men's traditional dress is somewhat like a loose robe, covering from the neck to the ankles.

3rd Requirement: Thickness:
The Prophet Muhammad once warned that in later generations, there would be people "who are dressed yet naked." See-through clothing is not modest, for either men or women. The clothing must be thick enough so that the color of the skin it covers is not visible, nor the shape of the body underneath.

4th Requirement: Overall appearance:
The overall appearance of a person should be dignified and modest. Shiny, flashy clothing may technically meet the above requirements, but defeat the purpose of overall modesty.

5th Requirement: Not imitating others:
Islam encourages people to be proud of who they are. Muslims should look like Muslims, and not like mere imitations of people of other faiths around them. Women should be proud of their femininity and not dress like men. And men should be proud of their masculinity and not try to imitate women in their dress. For this reason, Muslim men are forbidden from wearing gold or silk, as these are considered feminine accessories.

6th Requirement: Decent but not flashy:
The Quran describes that clothing is meant to cover our private areas, and be an adornment (Quran 7:26). Clothing worn by Muslims should be clean and decent, neither excessively fancy nor ragged. One should not dress in order to gain the admiration or sympathy of others.

Beyond the Clothing: Behaviors and Manners:
Islamic clothing is but one aspect of modesty. More importantly, one must be modest in behavior, manners, speech and appearance in public. Dress is only one aspect of the total being, and merely reflects what is present on the inside of a person's heart.