What were the fashions for clothing when Shakespeare was alive?

Just as it did in the fourteenth century of Chaucer's Canterbury Tales, clothing depicted one's social standing during the Renaissance, as well.

During the Elizabethan Age, fashion was dictated by the Sumptuary Laws, a set of laws that put limits upon expenditures. In fact, clothing informed much about the wearer since certain colors were reserved for certain people. For instance, such a color as purple was reserved for royalty, while crimson or scarlet, deep blue, black and pure white, gold, and silver were reserved for the highest nobility in a country. Only members of the Royal Family were permitted to wear ermine. Other furs, such as fox, of course, were worn only by the very wealthy.

Clothing of the upper classes was often heavy and restrictive. Women's gowns were full in the skirt; this skirt went over thick petticoats and corsets and underskirts with a tight-fitting bodice. Often the skirts were held up with hoops. It was quite acceptable to have a neckline that exposed the décolletage, but the legs were not to be exposed; stockings for the legs were usually knee-high. Frequently, the wealthy and the royalty, both men and women, wore ruffs, especially on grand occasions or for portraits.

Wealthy men wore stockings that went over the knees; a poufy knee-length trouser fitted over these. The jerkin was a type of shirt and over it was worn a doublet which had no sleeves. There were no collar or cuffs; often lace was worn or a ruff on the neck.
The clothing of the wealthy was made of brighter or darker colors as they were more costly to produce; the materials used were silk, satin, velvet, and brocade for dresses, and for men's clothing leather was often used, as well. The expensive fabrics such as silk and velvet were imported.

The lower classes worn much less clothing than the wealthy, of course. Their clothing was usually made of wool, linen, or sheepskin. (Cotton was prohibited in England to keep wool in production.) Clothing was in lighter colors such as yellow, russet, orange, green, pale blue, and even pink.