You can download a distribution of Groovy from this site
Once you've download the distribution, please read the installation instructions.
If you want to grab just a jar of groovy to embed in your application then try using Maven as your build tool and it'll download it for you or you can grab a groovy-all-1.0-jsr-<VERSION>.jar from the jar repository.
You could use the snapshot version if you like, this is rebuilt every time a change is made in CVS by our continuous integration build.
If you're happy to work directly with Maven then either download a source distribution or grab the code from SVN