First of all, this is the best way I know to learn new skills and to understand how Joomla works. You are not giving back, but getting back a lot as well. Disclosure: I am a Joomla Bug Squad (JBS) member.
Read more on the JBS Portal Page. To get a general idea, review all the articles from the portal page. It should give you a general overview.
How can we in the community get involved in testing?
The answer is simpler than you think: by testing, by using Joomla before it's GA (general availability). You can start reviewing the proposed betas or RCs for a specific version. Just install them on your own development / test installations and check if there are issues.
Report on the tracker for any issues you encounter. Check first if you are the first one reporting this or if this a older known issue is.
Are there specific prescribed test-case scenarios?
Generally you need to use your own business needs and test against them.
Testing is required on proposed fixes for known bugs or on new features. Each bug fix must have two people who tested it. This is actually an area where the the JBS is overwhelmed and needs as much help as it can get. Updates and new installations are also important. You will never run out of things to do.
Is the JBS looking for folks with specific skill-sets? If yes, which skill-sets?
Yes, all skill-sets :)
The Joomla! Bug Squad (JBS) is a team within the Production Working Groups. Their job is to identify and fix bugs in Joomla. See more at Introduction to the Joomla! Bug Squad
The idea is that you can get involved no matter your skill-set.
So how can I start, do I need to be a JBS member?
No, you don't need to. You can start by checking the Joomla Issue Tracker
You can help by (setting the filter status) looking into issues that are:
Open - issues that are not confirmed. Follow the replication instructions and see if you can replicate the issue.
Pending - issues that are generally confirmed and have a fix. Try to replicate the issue and than apply the proposed patch. See if everything works good.
If after you've read an issue you feel that you understand it, look into it. If it's another language for you, just move on. There are all types of issues.
Got more questions?
If it fits the format for stackexchange ask it here, otherwise you can ask them in the CMS Development Group.