How to find out if my specific idea is really new, or if someone has already worked on it?
What I find most critical: figure out the nomenclature. Look for articles about your research question in your own words and create a list of keywords that are frequently used. There is usually no consensus, so you will end up with synonyms. 

Once you know the words used by the community in your field to describe the concepts and problems, literature searches get a lot easier. My usual approach is to use a large database of publications (in my field Medline is good, I guess your field has its equivalent) and look for the few keywords I listed. Now, don't read all articles of course, do a selection based on the title first, then on the abstract. There is a lot of redundancy in published papers so you will be able to weed out a majority of the papers at this point.

In some fields, senior researchers sometimes write review articles that list the 'open problems' in the field. Even if they don't give such a list, good review papers give an overview of the state of the art and are a great source of secondary citations.

Of course, discuss the matter with your colleagues and adviser, read prominent blogs and if possible go to (a) good conference(s). Conferences are great to grasp what others do and don't, and they help to make sure you don't reinvent the wheel. 

Finally, I think you shouldn't worry too much at this point, here are a few words form my answer to this question Is there any research on the prevalence of academic theft?


  The chances that your idea is absolutely original is close to zero. Concepts, ideas and theories are almost always due to an
  intellectual environment in which many researchers are present. Even
  theories traditionally attributed to a single individual [...] were the result of
  inputs from several individuals over several years.
  
  The chances that your state of research, access to resources and previous intellectual work is similar for someone else is very small.
  Research breakthrough are a result of the right coincidence of
  opportunity, resources and intellectual maturity.