A good starting point for Groovy is http://groovy.codehaus.org/Documentation. A google search for specific questions is good, too. You could even use all kinds of Java documentation, because you could use Java code nearly unchanged for groovy.
For the JIRA API as a reference you could start here https://developer.atlassian.com/static/
Another excellent starting point is the source of the built-in scripts of the Script Runner plugin.
The use of a test system is highly recommended for testing your scripts, because through the scripts you are able to stop or corrupt the JIRA system.
And last but not least, on Atlassian Answers there are a lot of nice people which are happy to help you. :-) Just describe what you want to accomplish, what code you already have and maybe what error messages you find in the log (catalina.out)
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