On the Commission website http://ec.europa.eu/stages/index_en.htm you can find all the relevant informations about the application and selection procedures. Read it carefully before applying!
An useful .pdf file could be: http://www.ukrep.be/stage.pdf
Tips & tricks
In the application form, when choosing the Directorates or Services within you would like to work, focus on the ones that suit best with your academic and professional background!
Avoid choosing an area of activity that doesn't have any relevance with your background, but you'll be happy to work in.
Before applying, have a look on the organizational charts of each Directorate General or Service http://ec.europa.eu/dgs_en.htm