Bandcamp is a good start in finding underground artists online. Just scroll down towards the bottom of the home page and then filter what genre of music interests you and then seek/discover to your hearts desire.
https://bandcamp.com/
Depending on where you're located, seek out venues that host live music specifically catering to "underground" acts if possible. Usually smaller venues like bars, social clubs, etc. will host those types of acts from time to time.
If you have a local music store that sells vinyl, cd's, etc. That can also be a good source of finding new/interesting underground bands. Particularly if an employee that is also into that scene can be your guide in finding new music.