What do you mean "off the screen"?
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
What model phone do you have? Which messaging app are you using?
Normally, you can tap on the icon for your messaging app, and it will list all of your conversations, and if you tap on one, it will show all of the messages in that conversation. Then you can tap a back button on the top-left to get back to the full list of all of your conversations. I hope that helps!
If you're trying to look at older messages in a thread then you just have to swipe from the top to the bottom of the screen. This will move take you to the top of the messages. If they haven't been auto deleted by the device according to the settings keep swiping from top to bottom until you find the messages that you are looking for.