As far as the show goes, unfortunately there is not a lot of material to theorize on, since gooseworx can't shut the fuck up and keeps confirming shit on tumblr instead of the actual show, I'll use the tumblr trivia as facts just because, since they are not in the show they aren't really canon and can change whenever.
what is The Amazing Digital Circus?
The Amazing Digital Circus is a hyper augmented reality game running exclusively in one single computer in an office building of a company known as “C&A”, some have theorised C&A is Cain And Abel, with Caine actually being the creator of the game, this is false since Caine is an acronym for Creative Artificial Intelligence Networking Entity, which means he is not a human being and just a barely functional AI who is sentient of his own condition.
how does one enter the TADC?
No one knows. Of course, the physical action is just plugging the headset in your head, this automatically erases all the memories of the individual such as his name and physical appearance, but how does one come across this computer is not known. All the characters in the show come from extremely different backgrounds and ages, Kinger is 48 and a computer science specialist while Jax is a farm boy and only 22. My best guess would be that it happens just by pure luck and currently the company known as “C&A” is no longer active or does not know about TADC, the question of how is this sci-fi abomination running on a PC from the 90's or early 2000's is also completely open.