The first step is to connect with others. There are many different kinds of networks: by profession (e.g. engineers), by subject (e.g. numismatics), by function (e.g.. self publishing, statistics), by type (e.g. academic, independent scholar).
Find out are there any groups in your geographical area or country and join up. Libraries and archives are good places to find out about groups.
In order to create an online presence, have a look at LinkedIn , for instance, where there might be an appropriate group (such as Local History, Independent Researchers, Military History, whatever). (How to join a LinkedIn group or How to find the ones that suit you best).
You should definitely create your own Academia or a Google Scholar page (or both), even if you only have one or two publications (even reviews). Having a list to which you can add publications can be a spur to producing more!
The next step, if you want to go further, is to start lecturing or publishing. This way you get your name out there as someone who is an expert in your particular interest. The key here is to be enthusiastic about your topic and interested in others too (see, for example, Kristina Busse’s article on ‘How to be an independent scholar‘ or Kimm Curran’s ‘Reflections and resolutions of an independent scholar‘). After a while you’ll get a name and be asked to contribute to conferences etc. Have a look any journals or periodicals (Google your general topic or browse JSTOR to see whether there’s a journal that fits your area) and see what might be required to send in an article.
Just in case you think that independent research is limited to the humanities, here’s a post by a scientist. Another page at BrightworkCoResearch is about becoming an independent research, and also a case study talking with Cathal Garvey of IndieBiotech. On Quora there’s a very useful page about becoming an independent researcher from the get go with lots of tips.
I get the impression from the internet, however, that ‘independent scholar’ seem to refer to humanities-based studies. Whether this is the case or not, the general view seems to be that independents get on with it rather than re-thinking the academy and so on. I have no doubt that whether you call yourself a scholar or a researcher, doors will open if your work is of a high standard and you achieve sufficient visibility. In 2014 Pamela O. Long, historian of late medieval and Renaissance history, science and technology, was awarded a prestigious MacArthur fellowship. Now in her seventies, Pamela credits persistence and long hours for her success; she keeps her research going through grant funding.
Have a look at the National Coalition of Independent Scholars (USA), Canadian Academy of Independent Scholars, or search online for other organisations around the world.