The first step is heavily impacted by the module system and you need to know a little bit about it, but it doesn't come from adding modules. It comes from taking your existing Java-8-application and making it work on Java 9+. This step isn't optional and while you can work on it in increments, getting half the way to your goal gets you nothing - you can't be "Java 8.5"-compatible. ;) See my Java 11 migration guide for details on what to expect. Summary:
removal of Java EE modules
illegal access to internal APIs
removal of deprecated APIs and JavaFX
casting to URLClassLoader
new version strings
The second step, taking your Java 9+ application and turning it into modules, can be done incrementally. You can have half your JARs be modules and will reap about half the benefits (I don't have a good source at hand that explains this succinctly). Regarding the benefits, have a look at this thread.