All text for a project/story is stored in a single file, so it's essential to copy this file to the new computer.
There are many ways to do this including using a USB or thumb drive, sending an email with an attachment or using a cloud service like Dropbox.
Each project/story file name ends in .wnwx and in a file manager they are shown as WNWX files.
This shows the example project file in Windows file manager.
The project has more details on moving files in the section Help -> Miscellaneous -> Transferring to a new computer.
The short PDF manual has a section on this in chapter 9.
The detailed PDF manual has a section on this in Appendix C Backing Up and Transferring a Project.
On a Windows PC
This video shows how to move project files to a USB drive on a PC.
On a Mac
This video shows how to move project files to a USB drive on a Mac.
The Windows File Manager
The name and path of your currently open project is shown in the top left of WriteItNow
To show the Windows file manager press Ctrl and E