drop down tab. A bar appears at the very top of the screen (i believe its called a toast notification). You can click on it to launch whatever the notification is or ignore it and it will disappear. You can also slide it to the left or right to get rid of the notification quicker.
Yes, the phone will ding/vibrate if you have it active for; texts, emails, missed calls, other alerts. And when you power on, the lock screen will show how many of each are waiting for you