Open the Messages app on your iPhone
Find the conversation you want to print
Take screenshots of the conversation
Save the screenshots to Photos
Open the Photos app
Select the screenshots
Tap the Share button
Tap Print
Choose your AirPrint-enabled printer
Adjust print settings if needed
Tap Print
If you need a full conversation, use a Mac or PC to export the messages first
On a Mac, open Messages, select the conversation, then print from the File menu
On a PC, use an iPhone backup or third-party tool to export the text messages, then print the exported file