If you invent a new word, how do you go about getting this recognised as a real word in dictionaries?
Words are added to a dictionary on the basis of their usage. Before it gets into the dictionary, the word is carefully monitored to see if people use it often and how they use it (context).
Here is a link to an article that explains how a word is added to the Merriam-Webster dictionary.
I would say that any word is a "real" word if it is in some sense established and those using it have a shared concept of what it means. Whether particular dictionaries decide or not to include that word is their problem; it doesn't affect the reality or non-reality of that word. After all, the human species was speaking languages for thousands of years before the first dictionary was invented...
As for the question of on what criteria particular dictionaries decide to include words, this is really specific to the dictionary in question. In more technical dictionaries, or technical words in general dictionaries, it is usually a question of which words the consultant(s) decide ought to be included. For more general language, there's often a sense that some number of clear, attributable examples must be available (so an example where it is clear that the word is in some kind of "mainstream" use, and where its meaning is clear from the context).
If you have coined/come across a word that is in some kind of "accepted" use and you think ought to be included in a particular dictionary, you could always contact its editors with your examples.
How you go about getting it into a dictionary is simple: write your own dictionary. ;-)
Seriously, it's simply that you don't "go about getting it recognized". You get it used by others. The more, the merrier... and finally, the Merriam(-Webster).
You can't do anything other than getting it out there, getting it used. Nobody said it'd be easy, you know.