It's always worth contacting the dissertation adviser. Aside from that option, dissertations are increasingly available online, typically requiring interlibrary loan services. The company involved is called ProQuest here. Their search form returns this kind of header, followed by a lengthy abstract:
A topological construction of Vassiliev style invariants of links Day, Colin; Stasheff, James D. The University of North Carolina at Chapel Hill, 1993. 1993. 9324015.
To get beyond this public listing, direct purchase or interlibrary loan access then has to be used (which I haven't actually done). Keep in mind that most dissertations don't have lasting scholarly value in themselves. But Colin Day left mathematics soon after his degree and didn't publish further. I hosted his visit to our department when he was considering graduate schools and am saddened to hear of his premature death.