According to the University of Chicago Press, bibliography style is typically utilized for writings on history and the arts. It cites sources throughout the paper using either endnotes or footnotes---consult your professor as to which you should use---and includes a bibliography at the end of the paper with detailed source information.
Endnotes and footnotes include the same information---the only difference is where they appear in the paper. Either way, when citing a source, inserting either type of note on a word processing program does two things: it adds a small number next to the information you are citing, and then creates a place elsewhere where you may type in the citation. Footnotes appear at the bottom of the page, while endnotes appear in a single list at the end of the paper. For example, then, your first citation will have a small number "1" next to the sentence where you add it, and another number "1" will appear either at the bottom of the page or the end of the paper.
At the end of the paper, your sources are cited on a bibliography page---similar, in spirit, to a Modern Language Association (MLA) works-cited page. This is where you give detailed information for each source, listed in alphabetical order by last name of author.
According to the University of Richmond writing center, a typical note includes: "the author's full name, the title of the work, the specific reference (i.e., volume, if any, and page number), and facts of publication (i.e., place of publication, publisher, date of publication)."
Subsequent references may be shortened---if a note cites the same reference as the previous note, the Latin word "Ibid." is appropriate. Otherwise, later notes may simply give a shortened (though still recognizable) version of the title and a page.
Reference list style is the simpler, shorter method of Turabian---it is generally used more for various sciences.
Instead of footnotes or endnotes, this style utilizes short parenthetical citations---not unlike MLA style. Parenthetical citations typically include the most basic information: the author's last name, the year of publication and the page number.
Instead of a bibliography page, this style includes a reference list at the end of the paper---also on its own page. This list gives the detailed information for your sources, like the author's full name, the title of the publication and the publisher.