Be aware that there are several gotchas in this.
Check out the Template branch at https://sourceforge.net/p/swingjs/code/HEAD/tree/ into Eclipse 4.2 (Juno). Use "Check out as..." and call it something of your choice, probably not "Template"
You will need also the J2S compiler. This is in the j2s/plugins directory of that checkout, and it needs to be copied to the Eclipse Juno plugins directory. Restart Eclipse Juno.
Use project...build to build the project. This should run the J2S transpiler and create both a Java version and .js files for creating a JavaScript version. The JavaScript will not run in Eclipse directly. These are just starting-point files.
Refresh the project (right-click on project name, select "refresh"). This for some reason is necessary for Eclipse to list the JavaScript files in the bin directory.
Look in the bin directory and make sure there are .class and .js files there. Roughly one .js file for every .class file.
Run build_01_main.xml to create the site directory.
Outside of Eclipse, go to site/swingjs/examples/phet and try the applets there in a browser. There are many more applets you can try in the examples directory. Some of these are applications; some are applets. Both should run fine.
Note that you either need a local Apache server or you need to allow Chrome or Firefox to read files on your local drive. See http://wiki.jmol.org/index.php/Troubleshooting/Local_Files#Accessing_J.28S.29mol-containing_webpages_in_local_disk.2C_or_loading_models_from_local_files
If that all works, you are ready to add your src files to the project and see what you can learn. Note that you will need ALL the source code for your project. If you are using third-party JAR files, you will need their code as well.
Read through build_01_main so you have a sense of what it is doing.
To test your application, you need to add an HTML file in html/examples that will start your application. Take a look at some of the sample HTML files to see how that works.
Don't expect this to work the first time. SwingJS is really still at the "alpha" level -- working for us, but not fully described.
Better would be to give me a link to your project so that I can also build an Eclipse project and do some testing with you to give you pointers