If you're getting a ton of irrelevant results, it's helpful to find a word common to them and exclude it from results; I don't have an easy way of measuring how many relevant results are excluded but if you choose it well it'll help. Similarly, find some list of all the operators for a given search engine and try them out.
I've found searching multiple indexes can be helpful, especially ones that seek different categories of thing out. For instance if I can't find something using Google, Marginalia can be surprisingly helpful. A list
of sites to try is available here: https://seirdy.one/posts/2021/03/10/search-engines-with-own-....
Also, often finding some discussion of something that seems close to what you want and might discuss it briefly and seeing what it links to will help. But that's from mostly looking at academic stuff, which has copious citations that often won't show up in a search query for a term, but can be found in the likes of JSTOR or LibGen/SciHub.
Also from academic stuff: if you can find directories of things related to what you want (eg 'old books about the Standard Oil Company of New Jersey,' to take a real question I had), often a more general term ('old books') and then searching those websites (HathiTrust, Internet Archive, etc) directly will find things.
But that's for someone who primarily runs into trouble because I'm researching obscure subjects and probably are less applicable in other areas.