Review the student's sources. If he has used Internet sources, search the URL addresses and read the suspect passages of the dissertation against these sources to determine if he is too closely copying from and/or inappropriately citing these sources. If you find that the URL addresses lead to different sources or that the addresses lead to broken or out-of-date links, he may be trying to hide evidence of plagiarism.
If the student has not used web-based sources or you cannot find evidence of plagiarism based on the web sources she provided, type suspect phrases or paragraphs from the dissertation into an Internet search. If the student has plagiarized from a web source or from a print source that can be accessed via the Internet, your search should produce sources against which you can check the suspect portions of the dissertation.
If your web searches do not produce evidence of plagiarism but you still think that the student may have plagiarized, a more time-consuming option is to look up any print sources he has cited and read those against the suspect portion of the dissertation to determine if the student has committed an infraction.
Students may mask plagiarized sources through improper or missing citations. If you are unable to find a source for a passage you think may be plagiarized, turn to your departmental colleagues or colleagues on disciplinary listservs for help. Your colleagues may recognize the suspect information as coming from a source they have read before or are familiar with, and they can assist you in tracking down the original source.