What are the legal tournament formats for MtG?
You can visit the Banned / Restricted Lists for DCI-Sanctioned Magic: The Gathering Tournaments page to see a list of formats, plus deck construction rules and a list of banned/restricted cards for each format.

With the exception of prerelease Limited, new sets enter their appropriate formats on the day of their official release. The specific dates for upcoming sets are spelled out in the "New Releases" section of the most current Magic Tournament Rules (PDF link).

As for a description of each format, plus differences and defining characteristics, is probably overly broad as a question.