How to run java from macOS Catalina build 10.15.4?

In 2021 the easiest way is use brew and `jenv`

brew install jenv openjdk@11
jenv add /usr/local/opt/openjdk@11

And then add into Intellij IDEA a new SDK with the following path:

~/.jenv/versions/11/libexec/openjdk.jdk/Contents/Home/

I will also suggest to add in your .zshrc (or .bashrc)

export PATH="$HOME/.jenv/bin:$PATH"
eval "$(jenv init -)"
export JAVA_HOME="$HOME/.jenv/versions/`jenv version-name`"

Open System Preferences -> Security and Privacy -> General

You should see a warning about Java being blocked and you can click "Allow anyway"

The next time you run java you will get a confirmation message with the option to continue:

Java security confirmation