The "Fair Use Doctrine" is a legal defense to a claim of copyright infringement. Its goal is to help prevent a rigid application of copyright law that would stifle the very creativity the law was designed to encourage. At the heart of the defense are four factors which endeavor to determine if the use of the copyrighted work was fair:
Courts today tend to collapse the four fair use factors into two fundamental questions:
1) Is the use you want to make of another's work transformative -- that is, does it add value to and repurpose the work (or did just repeat the work for the same intent and value as the original)? Therefore, it is important when taking portions of a copyrighted work, to specifically consider:
2) Is the amount of material you want to use appropriate to achieve your transformative purpose?
Courts have also recognized, however, that non-transformative uses may be socially beneficial (for example making copies of a work for classroom distribution or using extensive quotes of a work in news reporting). Although transformative works are important and essential to protect, focusing exclusively on transformativeness when considering the scope of fair use risks losing sight that the doctrine exists to ensure that copyright law continues to serve the public interest by encouraging creativity and access to information.
Therefore, if you are commenting on, critiquing, or even parodying (imitating in a comical way) a copyrighted work, the use would lean toward being considered more fair as long as the you are demonstrating by your use a deference to the four factors previously mentioned. Additionally, research and scholarship, as well as nonprofit educational uses, are typically favored as fair use.
Given that, some argue that fair use is essentially directed toward educational use and therefore should be avoided altogether in a ministry context. However, the historical notes of the law seem to acknowledge a broader intent of the exception when the lawmakers wrote "Although the works and uses to which the doctrine of fair use is applicable are as broad as the copyright law itself, most of the discussion of section 107 has centered around questions of classroom reproduction, particularly photocopying."
That said, by its very nature this area of the Copyright law is intentionally ambiguous and vague. Lawmakers created the fair use exception to have an expansive meaning that could be open to interpretation and as such is typically applied on a case-by-case basis. This essentially means that the risk associated with invoking this exception is higher and that is why most would counsel to always seek permission when seeking to use any works which are protected by copyright.
If nothing else, especially don't buy the more common myths that "just covering" a song is fair use, or "as long as I'm not making money" it's fair use, or "if it's online (or YouTube), anyone can use it", or "as long as I give the author credit" it's fair use.