and both ask: How do you write text messages?

The important thing to get across when writing text messages is that the reader understands what they are reading. It needs to be clear that these are text messages. This can be achieved both verbally and visually.

Most writers already do this. The story says that the character's phone beeped, and they took out the phone to read the message. It's clear to the reader that they are now reading a message on the phone.

This become less clear when you mix in some actions. For example...

I looked at my phone. Jane had sent me a message. Meet me after school plz, it said. I lowered my phone. Why did she want to meet with me? Didn't we stop speaking to each other? My phone beeped again. She sent another message. It's urgent.

I read a traditionally published book that did text messages like the paragraph above. They were mixed in with actions, and while it felt realistic, the verbal cues were barely enough to keep me from getting confused. It needed visual cues as well. Italics are a great way to achieve this. Here's that same paragraph again...

I looked at my phone. Jane had sent me a message. Meet me after school plz, it said. I lowered my phone. Why did she want to meet with me? Didn't we stop speaking to each other? My phone beeped again. She sent another message. It's urgent.

Now it's apparent just by looking at the paragraph which parts are the text message.

Much like regular dialogue, alternating lines can signify a back-and-forth between two people, as long as you set up who the participants are, and who went first. For example...

I looked at my phone. Jane had sent me a message. Meet me after school plz.

I frowned with confusion. Didn't we stop speaking to each other? I sent her a reply. Why?

It's urgent.

But what did you want to talk about?

UGH CAN YOU STOP BEING SO DIFFICULT?

No need to shout at me.

Forget it. Now I want to shout at you for real.

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Another way to handle text message dialogue is to make it kind of look like one. Like this...

I looked at my phone and was surprised to see a text from Jane.

Jane: Meet me after school plz

Me: Why?

Jane: It's urgent

Me: But what did you want to talk about?

Jane: UGH CAN YOU STOP BEING SO DIFFICULT?

Me: No need to shout at me.

Jane: Forget it. Now I want to shout at you for real.

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You could make the names all-caps for further emphasis, if you'd like. There's no need to make it look exactly like a text message conversation, because the medium we are writing the story in is often limiting. It just needs to feel like one.