I am trying to add some light in a hall bathroom and wish to splice a wire from an existing fixture. This will be my first time and need some info.

Is there a specific question you have in mind? Or are looking for general information on how to do this type of project? If the latter, I suggest you start by purchasing a basic home wiring book - it will teach you about materials, tools, and techniques for projects like this. Then you can come back to the forum with whatever specific questions you may have.