Source: Harald Bøhn, Flickr (edited). All rights reserved
If possible, find the name of the university or other institution where the dissertation was written. This will make finding a copy much easier.
The resources below are listed roughly in order of usefulness. Fuller details of many of them are on the previous tab.
If you know the dissertation title, a simple search should find it. The content in ProQuest Dissertations & Theses Global: Humanities and Social Sciences and EthOS (for UK doctoral theses) should all be included in Summon, but a separate search to double-check might be worthwhile.
Try this next - Global ETD searches widely online for free copies of dissertations.
Next, check if the relevant university or college has an online repository. You can search for a repository in OpenDOAR; if one is not listed there, look on the website of the home institution, including its library webpages. The repositories guide provides links to search engines for searching across many repositories at once, as well as general information about this kind of resource.
Contacting the author
Finally, you could look for contact details of the author online and approach them for a PDF. Authors may have many valid reasons for not wanting to send copies to people they do not know, so do not be offended if your request is declined or goes unanswered. Also expect the author to ask you to confirm in writing what you will do - and agree not to do - with any copy they are willing to provide.