Installing The Java Development Kit (JDK)

Windows

Download the Windows x64 download from Oracle here.

NOTE: Make sure that you download the Java Development Kit (JDK) not the Java Runtime Environment (JRE). The JRE only allows you to run java programs, in order to develop your own java programs you will need the JDK.

Run the installer that you just downloaded. Java will install in your "Program Files" folder. (You may also have a "java" folder in "Program Files (x86)" and you should ignore it because the java kit you are currently downloading will NOT install there.)
Add the path to the bin folder in the java folder that you just installed to your PATH environment variable. Make sure that it is the path to the bin folder and not the path to a file inside the bin folder. eg: C:\Program Files\Java\jdk-10.0.2\bin
Verify that you have successfully installed java.

Mac OS X

Make sure that you have installed Homebrew before proceeding! Look at the top of the resources page on this website for instructions on installing Homebrew.
Run the folloing command in the Terminal:

brew update

brew tap caskroom/cask

brew install Caskroom/cask/java

The commands running successfully looks like this:

Verify that you have successfully installed java.

Linux

Most distros use the openJDK instead of Oracle's. This can lead to some issues with JavaFx, so make sure you install the Oracle version by running the following commands according to your distribution (if yours isn't listed, you probably have the expertise to install the Oracle version of Java on your own):

Ubuntu, Debian, Mint (anything using the APT package manager):

        sudo add-apt-repository ppa:linuxuprising/java
        sudo apt update
        sudo apt install oracle-java10-installer

        # If you have other versions of java installed, run the following
        sudo update-alternatives --config java       # Select the option with Oracle java 10
        sudo update-alternatives --config javac      # Select the option with Oracle java 10

Fedora, CentOS (anything using RPM packages):

Install the rpm package here.

Run the following:

            rpm -ivh /path/to/installed/rpm  # May need sudo
            
            # Use the following commands to select Oracle Java 10 as the default
            alternatives --config java
            alternatives --config javac

Add the JDK's bin directory to your PATH environment variable, if necessary (not required if using methods listed above).
Verify that you have successfully installed java.

All Operating Systems

To confirm that your java installation was successful:

At the command prompt type java -version. You should get output on the next line like java version 10.0.2.
At the command prompt type javac -version. You should get output like javac 10.0.2.
The output should look something like this:

$ java --version
java version 10.0.2
Java(TM) SE Runtime Environment 18.3 (build 10.0.2+13)
Java HotSpot(TM) 64-Bit Server VM (build 10.0.2+13, mixed mode)
$ javac --version
javac 10.0.2

The version number should be "10.*.*" Where the * can be any number. An older version of java will not work for the purposes of this class!

Oracle's installation instructions

Oracle, the company that makes Java, has documentation here