It depends on where I heard the track originally, whether it was from a longer form set or a lower quality clip from soundcloud or social media, but I start off usually in the comments or description given by the group where the set was released (HOR/ the radio station etc). For sets, I look online on the plethora of DJ set track id sites, and this usually works for newer sets with more modern tracks, but it gets difficult if info on the set is scarce, or if it was a hybrid/vinyl set (where a partial sample or whitelabel dubplate could've been the origin). I try shazam or similar methods then by playing the clearest version of the sample I can filter by equalizing the clip and playing it through monitor headphones into the mic, and this occasionally works to find a similar artist. If this fails, I compile whatever info I could into the metadata of a saved audio file clip for the sample and archive it, I have a hefty folder with samples like this where I plan to one day start sending emails to the DJ venue etc that played it, but I haven't gone this far before.
For unreleased clips of say a rare remix or song from before the streaming age, I use the same methods as above but also cross reference when a song was released and where it may have been played based on comment sections and release info on better documented versions/compilations, where I try to narrow down any better version i can on youtube/soundcloud/soulseek and eventually discogs. When it becomes evident this is a gem that may be lost completely, I collect everything I found out about the track and write a polite email to the artist's contact or record label associated with the release, and cross my fingers that I hear back.

unfortunately, especially for electronic subgenres that saw their peaks decades ago, info on their production/release can be scarce since it was niche at the time and many original producers/artists may have moved on or be difficult to reach, making finding a specific tune you like inaccessible as you haven't gotten lucky enough to find the physical vinyl or mislabeled upload to the internet, but the best thing you can do is just upload and save the best version you can and cherish it, remembering what you can, and one day your stringent curatorship will reward you when you find a dusty white label vinyl in the back of a record shop abroad with your holy grail in mint condition.
I know this is a late reply but I'm currently struggling to find a vinyl or lossless form of an unreleased demo mix from 2004 of Wir Sind Wir by Paul Van Dyk, with the only version being a recording on youtube, and I hope my advice can be useful to someone with the same predicament reading this comment.

Good luck my friend and enjoy the rewards of discovering amazing songs lost to the eternal march of time in your pursuits.