Most group boards have instructions on how to join. Just follow them. In absence of an instruction, leave a note on the owner's latest pin and ask for an invite. Use the @name format so that the owner receives an email that you left her a message.
One way to find boards is to look for an active pinner in your niche and check out their profile. Chances are, they're pinning to group boards. Also, there's a Google search string floating around in this forum on how to find group boards. Just have to find it.