Trying to do this in Arc 9.3.1. Can't work out how to make it visible.
Where does the issue occur?
This article should walk you step-by-step through the process:
Creating a New Layer from Selected Features
And if not, here is a video with the same process (specifically for 9.3.1).
ArcMap - ArcGIS 9.3.1 - Creating Layer From Selected Features - YouTube
If you want to create a new feature class of just the selected features in a feature class:
If you would instead like to create a Selection Layer:
ArcGIS Desktop Help 9.3 - Using selection layers
Chris Donohue, GISP