I don't think that the research process is different for academics and non-academics since most databases are publicly available (although the actual papers might be not).
If you have already found a paper on your topic, locate that paper in a field-specific database (e.g. RePEc for economics, IEEE for computer science, the Web of Science for a more general database, PubMed for medicine, ...) and look at cited and citing articles which are relevant. Also, search for other publications by the same author.
If you don't have a paper on the topic: I believe that some databases offer a list of keywords, so you might wanna look at that list and see if anything relevant pops up.