Why do I have a crescent moon next to the time on my iphone?

And how do I get rid of it?

It's Do not disturb mode. You don't get notifications for missed calls and such.
Just go to settings and turn it off

That means your iPhone is in "Do Not Disturb" mode which will cause you to not be alerted when you get a notification (such as a phone call, message, Facebook/twitter notification).
To turn this on or off, go to:
Settings < Do Not Disturb < "ON" or "OFF"
You can also edit the times you want "Do Not Disturb" to be on by going to
Settings < Notifications < Do Not Disturb
Hope this helps

That's the symbol for Do Not Disturb, a new iOS 6 feature that does what the name describes. Disables notifications/calls during the time it is active.
The setting to turn it off is easily found in the Settings app.

How do I go to "settings"?

Ok I went to settings & do not disturb is not on -- but yet under 2 of my messages I still have the half moon why

I have a IPhone 6 lately a number of emails are going into JUNK- Can't figure out why?