Trust us, there is no easy way of exporting text messages from an iPhone to a format that is suitable for printing.
You can create screenshots, you may argue, but if we're talking about a text conversation with hundreds of messages then forget about it. It's doable, of course, but it will take forever.
You could try and send the text messages as emails but all you are going to get is a mess of plain text files with no time stamps nor any other relevant details. Readable? Yes. Usable? Barely. Believe us, we tried.
There are tons of so-called text exporters in the iOS App Store but some are misleading and they all require a computer anyway. Most of these apps aren't free and don't even have trial versions. Your hard earned cash is on the line whenever you risk trying these out.