I've checked back a number of pages and can't find anything on this but I'm sure I'm not the first to ask.

So I want to write a scene where the protag has a conversation through messages on his phone.  I was wondering how best to do this?

Would it be a slug indicating the phones screen like...

He takes out his phone and begins to type
INSERT PHONE SCREEN or CLOSE ON PHONE

But then how would I indicate who was saying what?  Would I simply use normal dialogue...

                     DAVID
           Hi how's it going?

                     AMY
           Fine. What's up?

or bullet it like...

DAVID: Hi how's it going?
AMY: Fine. What's up?

I've never done this so I'm a bit lost lol

The short answer is anything that makes it clear.

I have seen two approaches. This one simply says state that what comes next will be text/IM and then write it in italics. Here is the link:

http://johnaugust.com/2011/handling-ims-in-screenplays

Trottier recommends centering the message and putting it in quotations. Here is the link:

https://www.keepwriting.com/tsc/textinginmovies.htm

Although Trottier is generally my go to - I disagree with him here and I prefer the first approach. Again - as long as you make it clear you are okay.

Cheers for the help, dave.

no worries

You could also try

INSERT: Phone screen TXT Message

                   DAVID
           Hi how's it going?

                     AMY
           Fine. What's up?

BACK TO SCENE

As Dave said, they key is that it's clear to the reader.

Anthony

I've gone for this, what do you think?

INSERT: PHONE SCREEN

                        DAVID [TEXT]
                Hi, it's me.

                        AMY [TEXT]
                What have you forgotten?

BACK TO SCENE

If you never cut away then voice over. Voice over if the person you see isn't the talking but keying in and voice over the reply. If the person is talking while typing in then don't. You can voice over like "see you in an hour, smiley face, smiley face, a bunch of exclamation marks!" If you want to see the text, then insert, but I wouldn't unless it's important to see the text. Go read You've Got Mail and see how Efron wrote. Same kind of thing. I would not clutter the story with inserts back to scenes.

Quoted Text I've gone for this, what do you think? INSERT: PHONE SCREEN                         DAVID [TEXT]                 Hi, it's me.                         AMY [TEXT]                 What have you forgotten?

It works for me - although I would consider putting the dialogue in italics or quotes

italics, nice idea, dave.