After refreshing they should be ready to use, but first make sure you have a Groovy source directory created (delete 'java' directory if there is one, it isn't needed) and write some (or much) Groovy code there. Annotate every Groovy file with @CompileStatic.
When you have finished writing and testing your mod, run "build" as always, then run "createClassHierarchy" and "remapFieldNames". createClassHierarchy will make class-to-superclass mappings and class-to-field mappings. remapFieldNames will use these mappings to create a Jar with a classifier "fixed" from the original Jar. You can change the classifier of the produced Jar to something else.
You also should be able to write mixed Java/Groovy code.
To play the mod, the players will just need to get Groovy library from its binaries from official website and put it into 'mods'.
Under the hood
Groovy uses a thingy called 'meta object protocol' which compiles its code differently from Java. We don't want that, because it "hides" class fields from Forge's obfuscation tasks. So we annotate every Groovy file with @CompileStatic, which makes code to compile almost in the same way as Java does. Groovy also sets fields by their names (similarly to getting/setting a field via reflection), not references, thus obfuscation tasks can't find them. This plugin takes care of finding such unobfuscated fields and obfuscates them.