You may want to print your messages for various reasons. You can easily copy and paste individual text messages but please note that there is no direct way to print text message conversations. However, if you like to obtain a copy of all your iPhone/iPad (i)Messages for any purposes, you may use the following methods! 
Method 1 For Printing Message App iMessage & SMS Text Conversations
Take a screenshot of the messages you want and print that screenshot!
To capture your iPhone’s or iPad’s screen
- For iPhone X, press and hold both the Volume Up and the Side Button at the same time
- For older model iPhones, iPads, and iPod Touch, press your Home button and Power/Lock/Sleep button at the same time
- Or use Assistive Touch on all models to take a screenshot with one hand!
Depending on your sound settings, you might also hear the camera shutter sound when your screen is captured. Then open your Photos app (or camera roll), find the screenshot (look for a screenshots album) and print it.
If you need to print your text messages for legal purposes, it’s best to capture screenshots of all the text messages so they are time-stamped and then print the screenshots. And don’t delete ANY of those messages and make sure you backup your iDevice using iCloud AND iTunes, if possible.
Method 2 For Printing Message App iMessage & SMS Text Conversations
- Locate the text message you want to print
- Press and Hold on a text box until a menu pop-up with the following options: Copy, Speak, More
- Choose More
- Tap the circles next to each conversation thread you want to print
- Once all conversations are selected, tap the forward arrow button at the bottom right of your screen
- Forward the messages to yourself
- A new text arrives that contains all the conversations you want to print
- Press and hold on that new message and select Copy from the pop-up menu
- Open a new app, like Mail, Notes, Reminders, or something similar and paste that copied information
- Print from your chosen app using that app’s printing feature (often in the Share Sheet Button or located in menu options of the Forward Button)
- Must have a printer that supports AirPrint to print from an iPhone, iPad, or iPod Touch OR an app that supports your printer
- Must have a printer that supports AirPrint to print from an iPhone, iPad, or iPod Touch OR an app that supports your printer
How to Print Texts Using Legacy iOS versions
- Locate the message(s) you want to print
- Tap Edit
- Check the circle buttons beside each item
- Tap Forward and send the selected messages to yourself
- When you receive the message you just sent, tap and hold to copy and paste somewhere else (e.g. Notes app) and print