To get ghostwriting in Phasmophobia, all you need to do is pick up the book and place it in the location where you think the ghost is or roams past.
At first, expect the ghost not to start touching or doing anything with the book right away. It's common for the ghost to do this, but eventually, you may get something.
A good thing to do is place the book, sitting straight up, and then a video camera in front of it. Doing so will allow you or a friend in the van to monitor the book for when the ghost starts writing.
Related: Do Footprints Count as Fingerprints in Phasmophobia?
If you don't get anything for a while, simply pick up the book and try another location. Causing some ghost activity and asking for the ghost to write in the book or even "can you give us a sign" may help.
Continue doing this for a few minutes or until something major happens, like a hunt or other ghost activity. You can also take a moment to narrow down the evidence list and leave the book alone as the ghost may write it in it while you are not looking.
If the ghost has still not written in the book even after all of this, you are probably safe marking it off the checklist.
For more on Phasmophobia. we recommend checking out Phasmophobia Ghost Trigger Phrases and How to use the Spirit Box in Phasmophobia.