This question is actually very hard to answer in regard to one aspect...the Contemporary Period. Given that the Contemporary period is "now", the characteristics are, basically, yet to be determined.
The Contemporary Period, given it is a current movement, is happening now. Therefore, until a new movement begins, it is very hard to actually define the typical characteristics of Contemporary writers. That being said, one could begin to define what the typical themes of this movement are.
Today's writers seem to be defined by their ability to speak to the new generation of readers. The genre is filled by the influence of today's media and trends. For example, the supernatural movement has exploded in the last 10 years (think Harry Potter and Twilight). Another typical theme of this period deals with the struggles of today's youth (think The Hunger Games and Crank).
The Contemporary movement is then defined by all types of characterizations, themes, and (unfortunately) stereotypes and generalizations. Fortunately, the Contemporary period has allowed new readers to find material in which they can relate to- bullying, alienation, self-preservation, and escape.
As for the Modern Literary Period, this movement is much easier to define given it has already existed and been defined by critics and readers alike.
Typical characteristics of the Modern Period include the quest for the "American Dream" (which includes pride in Nationalism and individualism) while embracing optimism in ones own future and dreams. Given this period began with the onset of a new century (1900s), literature and arts focused on technological advancement and class control because of the ever changing population.