How can I join/volunteer a research group for short term?
If you want to do it as a hobby you should look for "citizen science groups" near you or in your area of interest. See the Wiki article to get an idea.


  Citizen science (also known as community science, crowd science, crowd-sourced science, civic science, volunteer monitoring or networked science) is scientific research conducted, in whole or in part, by amateur (or nonprofessional) scientists.


If you want to participate in research at universities and research institutes I would just try to contact the group(s) there that work on the topics of you are interest in.
I guess plenty of groups would be happy to have someone to do some research assistant work and for you it would be a possibility to get to know them and their work.