Since most answers are out of date, here's what works as of end of 2018 under the assumption that
In that case, grab the desired version from one the many available, freely usable OpenJDK editions, e.g.:
Some of these include installers, but if not you can do the following. Assuming here version 11.0.1 for Mac. In your favorite shell, run:
tar -xzf openjdk-11.0.1_osx-x64_bin.tar.gz
sudo mv jdk-11.0.1.jdk /Library/Java/JavaVirtualMachines
# Fix owner and group
sudo chown -R root:wheel /Library/Java/JavaVirtualMachines/jdk-11.0.1.jdk
# (Optional) Check if the new JDK can be found
/usr/libexec/java_home
=> /Library/Java/JavaVirtualMachines/jdk-11.0.1.jdk/Contents/Home
[0] Note that the Oracle branded JDK has significant licensing restrictions allowing you its use basically only for testing, i.e., not for production. If you do not have a support agreement with Oracle, then it seems risky to me to use their JDK, especially since the differences to OpenJDK are minimal.
Edit: added more choices