http://www.soapui.org/about-soapui/soapui-faq.html#1-SoapUI--General-Questions
3.1.1. What is Groovy?
It's a scripting language which is very similar to Java. read more here.
3.1.2. Where can I learn Groovy?
Here is an excellent guide to get started if you're a beginner.
3.1.3. How do I know which objects and methods I can use from Groovy?
You need to have a look at the API. It's pretty techical, but once you get your head around it, it will be your scripting bible.
3.1.4. Is there a collection of Tips & Tricks for SoapUI scripts?
Yes, glad you asked! You can find it here.