We assume, the application server is already configured. The next step is to configure an exploded WAR artifact for the web project. An exploded WAR is a decompressed web application archive, a directory structure that is ready for deployment on an application server. IntelliJ creates it automatically, but nevertheless, you should go to File --> Project Structure --> Artefacts and ensure that the exploded web application ends with the extension .war. If you use Maven, the exploded WAR is created below the target folder. More info on the help page.
You should also check if the Hot Swap is enabled. Go to the File --> Settings --> Debugger --> HotSwap and ensure that all checkboxes are checked and the radio button "Reload classes after compilation" is set to "Always".
Hot deployment for changed Java classes is resticted by JVM. E.g. the hot deployment for classes with changed method signature(s) doesn't work. But if you changed a method body, it will work. So, if you don't use JRebel which allows the hot deployment for classes being structurally modified, you can still rely on IntelliJ. All what you need to do for changes in Java classes is to recompile them. For that, you can go to the menu Build --> Compile or simple hit Ctrl + Shift + F9. After that, go to the browser and refresh the page to see changes.