There are numerous reasons to monitor a court case and, there are a few ways to do it.

First off, as we live in a super transparent democracy, the information on most court cases are available. The exceptions are for sealed cases and probably, ironically, public figures/politicians.

The first and generally most critical thing you need is the location of the case. The location includes the physical location and type of court.

Once you locate the court, the first thing you want to do is go to that court's website.

As you can see, there are three courts in Queens Co., NY

Each site is a little different. Don't be afraid to contact the Office of the Court Clerk for help. They will help you to the extent that they are allowed to.

For the example, I picked the Queens Co., Supreme Court.

I'm not sure what kind of Court the Queens Co., Supreme Court holds. What I did though was click on Library then, Decisions and,

I got here:

All that is actually a lot of stuff for at least the NYC area

Pacer

For Federal Cases like Hulk Hogan vs Gawker, you're going to need Pacer. Signing up for Pacer is pretty easy. You get 150 pages free per quarter.

As you have to pay, you have to give them some information. All of your information actually. One way to give a little less information - to avoid giving your payment information - you can opt to have them mail you a confirmation and a password. If you go over the 150 pages in a quarter, you're still going to have to pony up your credit card info. They don't take monero.

Pacer

It's a good system

https://www.pacer.gov/login.html

Happy Hunting