Wondering if anyone would be kind enough to advise how I would go about tracing a clergyman's records from Glasgow?
It depends entirely on which denomination he belonged to. There are umpteen presbyterian denominations, each of which kept its own records.
See
http://website.lineone.net/~davghalgh/churchhistory.html to get some idea of the complications. Note that this contains only the presbyterian denominations, though as your man was a presbyterian missionary he was almost certainly affiliated to one of those.
All of those denominations would have had their own hierarchy of kirk session, presbytery, synod and general assembly. The Church of Scotland's Presbytery of Glasgow will not have records of a minister affiliated to the Free Church of Scotland's Presbytery of Glasgow, and vice versa.
The first port of call is
Fasti Ecclesiae Scoticanae, as already suggested. This contains brief biographies of all the ministers of the Church of Scotland.
As he supplied testimonials from a Faculty of Arts and Divinity, it sounds as if he studied at a university. The universities do generally keep records of their students, but you need to know which university. The University of Glasgow has a web site listing all its graduates up to 1914:
http://www.universitystory.gla.ac.uk/search/. The University Archives also have records of students who, for whatever reason, did not progress to a degree. Be aware, however, that the Free Churches had their own colleges for training ministers. Also, he may have taken a first degree at another university before going on to study divinity. It would be worth checking the printed 'Roll of Graduates of the University of Aberdeen' which is available in various libraries. If you draw blanks in both of those, you could contact the archives of the Universities of Edinburgh and St Andrews.
If it was the United Free Church, there is a history online at
http://www.ebooksread.com/authors-eng/robert-small/history-of-the-congregations-of-the-united-presbyterian-church-from-1733-to-1900-ala-402/page-45-history-of-the-congregations-of-the-united-presbyterian-church-from-1733-to-1900-ala-402.shtmlI discovered when trying to track a minister of the Free Church of Scotland who also emigrated (to Australia) that the Free Church archives had no useful information, but if George Hay belonged to the Free Church, there is a small chance that they might have something on him.
Although the 1881 census doesn't say what denomination he was affiliated to, it is possible that his marriage certificate might say so. If you don't have a copy of that, you can get one from
www.scotlandspeople.gov.uk at modest cost.