Groovy is supported natively in NetBeans IDE from NetBeans IDE 6.5 onwards. That means that you do NOT need to install any plugins of any kind if you want to code in Groovy in NetBeans IDE.
How To Get Started
The Groovy editor is a standard part of the "Java" distribution, i.e., the distribution aimed at Web development. Also included in that distribution is support for Grails. Click here to download the "Java" distribution, 6.5 or above:
http://www.netbeans.org/downloads/index.html
Note: The Groovy editor is not part of the Java SE distribution of NetBeans IDE, since that distribution is meant to be as small as possible. You are therefore advised to use the "Java" distribution instead, if you want to use Groovy. You will then, optionally, also be able to use Grails.
Creating a Groovy Application
Here is described how to use Groovy in NetBeans IDE:
http://www.netbeans.org/kb/docs/java/groovy-quickstart.html
Here's a screenshot showing a specific icon for Groovy files in the IDE:

Creating a Grails Application
Here is described how to use Groovy in NetBeans IDE:
http://www.netbeans.org/kb/docs/web/grails-quickstart.html
Creating a Griffon Application
Work is being done on Griffon support for NetBeans IDE too. A pre-alpha version of the support is available here:
http://plugins.netbeans.org/PluginPortal/faces/PluginDetailPage.jsp?pluginid=18664