Screen does not come on when a mesage arrives

[jim131]

I have just switched from using an Iphone for 5 years to Android, so please bear with me. I am not sure how on the Note 3 to get the screen to come on to notify me when a text messsage or email arrives? I have tried all kinds of settings, but unable to find where to enable notifications either in lockscreen or when the screen is off. Thanks for your help!