The first and foremost step is to determine the right branch for yourself. If you want to pursue a research internship some of the common options are
Once you have decided on the branch, contact the concerned professor and express your interest in working with him via email. If the professor agrees, there might be some additional formalities depending on if you are a student or not. As far as I know, you don’t require a recommendation letter. Seek help from the professor or the seniors regarding other formalities. The Academic sections in NIMHANS take care of all the formalities. You might have to pay some fees for doing the internship if you are not a student.
Hope this helps you!