The method for taking screenshots is holding both the power button and the volume down button at the same time for a few seconds except for Samsung devices. You don't mention which phone model you have.
The other option is to download a SMS Backup application from the Play Store to copy the messages into a format you can email to your computer and print from there.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.