When I started to get into private trackers I did the following, which worked out really well in my case:

1. Basic research (back then mostly via re*dit) on what the most popular trackers are and select the ones I want to join
2. Be prepared that being part of private trackers also means that one has to contribute back to the community by seeding
3. Hang out in their irc or discord channels and either wait for open invites or just be nice to other people and get invites from them (just trying to be part of the community)
4. be patient, it took a few days to get into the first one and after a month or two I was already in all of the trackers I wanted to be in

It was actually not much effort, I had to go through only one interview which was easy to prepare for and not very challenging. All in all it was definitely worth it and I'm glad I brought up that little bit of patience