Disclaimer: I am not a lawyer. This is a complicated area of law, but I'll give you the 30,000 foot view to get you started.
By default (at least, under U.S. law), each co-author owns an equal interest in the work's copyright. This is irrespective of how much (or how little) each co-author contributed to the work. So, absent of any agreement, if there are two authors, the split is 50/50, thirds for three authors, and so on.
For someone who collaborates on a work to be considered an "author," his contribution must be independently copyrightable. That means:
Someone who designs illustrations with the intent that they should be used in a specific book is a co-author (graphics designs are copyrightable)
Someone who composes the music for a song, or writes its lyrics, is a co-author (music and lyrics are copyrightable)
Someone who comes up with the general idea for a screenplay is not a co-author (ideas are not copyrightable)
Someone who researches population statistics for a geography textbook is not a co-author (facts are not copyrightable)
Someone who invents the algorithm for a new search engine (but does not write the actual computer code) is not a co-author (algorithms are non-copyrightable processes)
Each co-author can exploit the work in any way they seem fit (license the work, create derivative works, etc.), but they have to split all the profits with the other co-authors in equal parts. A co-author does not need to seek permission from the other co-author(s) to use the work, and likewise, a co-author cannot prevent the other co-author(s) from using the work.
An exception is the grant of an exclusive license, which requires the consent of all co-authors.
Co-authors' shares of a copyright are property interests that pass to their respective heirs.