How do I know when it's a "new day"?
For the purposes of continuing a streak and making sure I get some practice in everyday, how do I know when a new day is set?
Is it 24 hours since you last earned some points? Or is it midnight local time? And if it is midnight local time, where are the time settings that you can adjust so Duolingo matches your time zone? Sometimes I find my streaks randomly dissapear even though I'm pretty sure I've practiced that day.
Midnight according to the time zone you were in when you first opened your account.
You can learn more about how Streak and Streak Freeze work here: http://www.duolingo.com/comment/1426103
If you're sure you've kept up your studies everyday on time according to what you read, make sure to report the problem to Troubleshooting. You'll find info about how to do that here: http://www.duolingo.com/comment/1254215
Is there a way to view what time zone my account is set on? I may have set it wrong when I signed up, maybe that's why there's a discrepancy.
There is, but it is a bit tricky (but not hard)
Right click on the web browser, click on view page source
Do a Ctrl+F (page search) for the word timezone, and you will see something like this""timezone": "America/Chicago"", and that will give you your timezone.