How can I print text messages that are saved on my phone

"Email My Texts SMS" App does that!
It allows you to email them, save the email or print the email. It is easy to use.

Then just delete it

Hi zaylasmommy,
Depending on what phone model you are using, you can plug you're phone into your computer and use the Software which came with your phone on your computer to save the Text messages and then print them out.
but if your phone did not come with computer software then the only way to print out your Text message is to type it on your computer Manually and then print it out.

i hope this helps.