You should get something right away for the purpose of validating the email address on the form. If you didn't get that, then you should probably reapply.
If you did get that email, then it can take anywhere from a few days to a couple of months. If it's been as long as you say, though, your application may have been rejected. Some of the editors that review applications don't send out rejection notices, so you might not have heard anything if that was the case.
At any rate, since it's been about three months, I would reapply.
