I see here that there are a load of languages aside from Java that run on the JVM. I\'m a bit confused about the whole concept of other languages running in the JVM. So:
To an extent it is probably an 'Arms Race' against the .NET CLR.
But I think there are also genuine reasons for introducing new languages to the JVM, particularly when they will be run 'in parallel', you can use the right language for the right job, a scripting language like Groovy may be exactly what you need for your page presentation, whereas regular old Java is better for your business logic.
I'm going to leave someone more qualified to talk about what is required to write a new language/compiler.
As for how to writing code, you do it in notepad/vi as usual! (or use a development tool that supports the language if you want to do it the easy way.) Compiling will require a special compiler for the language that will interpret and compile it into bytecode.
Since java also produces bytecode technically you don't need to do anything special to run it.