While much of the world around us is subject to copyright laws, provisions in the Copyright Act protect many things bloggers typically want to do. Copyright law does not protect ideas nor does it protect facts. So a blogger is free to write a story about the same subject as another writer.
The Copyright Act also protects the "fair use" of copyrighted works by bloggers. (See the Fair Use page on this guide for more.) Bloggers may quote passages from a song, book, or other work in order to comment and criticize them. A history blogger discussing a new book on World War II could under the fair use doctrine quote from that book to show the author's facts are wrong or his style is unreadable. Bloggers may take an excerpt to report on the subject. For example, a blogger on music news covering the copyright infringement suit on the song "Blurred Lines" might have posted a clip under the fair use doctrine from "Blurred Lines" and the song it was alleged to have infringed, "Got to Give It Up," in order to report the story.
Linking to other websites is not copyright infringement, even if it is "deep linking" to features on a webpage. Using embed codes to display something from another website is also not infringement. See Flava Works, Inc. v. Gunter, 689 F. 3d 754 (7th Cir. 2012).
The Electronic Freedom Foundation has an excellent guide for copyright and intellectual property issues as part of their Legal Guide for Bloggers. They have information specifically for music bloggers receiving takedown notices under the Digitial Millennium Copyright Act.