There are a number of ways to do this.
The easiest, being that you have already set your work area using the "b" and "n" keys, would be to go under the "Composition" menu, and choose "Trim Comp To Work Area".
You can also use "alt/option [" or "alt/option ]" with the layer selected in the timeline in order to trim the ends of the layer.
Also, you can drag the ends of the layer (when you mouse over the ends of the layer, you'll see the cursor change) in, or out.
I must be doing something wrong. I have used the "B" and "N" keys and then
"Trim Comp to fit work area" - I then save this as a project. But when I
hit the "first Frame" in the video preview box, the darn thing returns me to
the very first frame, of the section that I thought I had deleted. Any
suggestions would be sincerely appreciated.
When you trimmed the comp to the work area, did you notice if your timeline is now the duration of your work area, or is your work area still only a small segment of the comp in which you're working?