What Netflix is saying
Very little, which shouldn't come as a surprise. (Netflix did not return Thrillist's request for comment on the renewal status at the time of publication.) The standard wait time between seasons for Netflix series isn't the same as network shows, which often get renewed or cancelled based on ratings data, which Netflix famously does not release. Judging by other metrics, The OA feels like more of a cult hit than a Stranger Things-style mainstream phenomenon.
Also, it's important to remember that The OA was developed, marketed, and distributed in an unconventional manner that involved very little pre-release hype. The project was initially announced in March of 2015, but most people didn't find out about it until the trailer "surprise-dropped" a few days before the show was released on December 16th. It's very possible that Netflix, along with Marling and Batmanglij, will try to keep an aura of secrecy about the second season as well.
So, what's a likely release date? Given the "take your time" approach offered to many of 2016's biggest hits -- both HBO's Westworld and FX's Atlanta won't return until 2018 -- it wouldn't be surprising if Marling and Batmanglij, two writers who seem especially meticulous and research-oriented, don't dive headfirst into a second season. The closest analogue might be Sense8, another sci-fi show with a devoted online fanbase, which debuted in 2015, had a Christmas special in 2016, and won't see the release of Season 2 until May 2017. That approach would give message-board-dwellers a chance to rewatch the first season a few more times.