The first question to ask is: Has copyright holder already granted a license for you to include their work. Sometimes authors have already provided permission through grants such as Creative Commons licenses. The license, itself, will identify the terms of what uses can be made without needing to get the author's permission first.
Published prior to 1923: Work is in the public domain.
Published 1923-1977: If the work was published without a © notice, it is in the public domain. If it was published with a © notice, but no registration renewal was ever filed, it is in the public domain.
Published 1978-present: Work likely not yet in the public domain. (Remember, copyright is usually life of the author + 70 years).
The purpose and character of the use, including whether the intended use is commercial vs. for nonprofit educational purposes. Tip: Uses in nonprofit educational institutions are more likely to be fair use than works used for commercial purposes. This may work in your favor for publishing the dissertation, but not necessarily a subsequent commercially-published monograph based on your dissertation. See the FAQs page for more detail.
The nature of the copyrighted work. Tip: Republishing factual work is more likely to be fair use than incorporating a creative, artistic work such as a musical composition.
The amount and significance of the portion used in relation to the entire work. Tip: Using smaller portions of a work is more likely to be fair use than larger portions, or portions that represent the "heart" of the underlying work
The amount and significance of the portion used in relation to the entire work. Tip: Uses which have no or little market impact on the copyright holder's ability to sell or license the original work are more likely to be fair. If the copyright holder offers licenses for uses similar to yours, use of the work without that license could harm the market for the license--weighing against fair use.