What are the conventions of comedy and tragedy in Shakespeare or literature in general?

The conventions in Shakespearean tragedy are largely the same as those identified by Aristotle. In Shakespeare, as in Aristotle's Poetics, a tragedy
has a sympathetic hero who is of noble birth, or more generally who begins the play in an elevated social position;
involves this character falling from grace and succumbing to disaster because of his own behavior;
showcases the character's "fatal flaw," which causes this behavior;
and provides some kind of catharsis for the audience.
In Shakespearean tragedy, the "disaster" is almost always a death; generally, Shakespeare's tragedies end in the deaths of not only the protagonist but several of those around him.
The elements of a Shakespearean comedy are rather less well defined. In the first place, a "comedy" may not be a comedy in modern terms--it is a "comedy" only in that it does not end in tragedy. Some of Shakespeare's comedies--like The Comedy of Errors--are closer to our modern understanding, with most scenes geared towards making the audience laugh. However, others, like As You Like It, contain a lot of dramatic material as well.
Elements frequently found in Shakespeare's comedies are, nonetheless, ones we still recognize in comedies today. Confusion and cases of mistaken identity form the basis for much Shakespearean comedy. Shakespearean comedies also frequently have romantic plots and end in a marriage.