The nut is the little piece that the strings pass through on their way out over the fret board from the peg head. It's important. I am making them out of white plastic bar stock from the hobby shop. Really hard wood works fine too (that's what the old Martins I've seen have), or you can get all fancy and use bone. I just think "white stuff" looks good :-).
First, sand the angle on the bottom to match the angle at which the peg head falls away:
Then mark a line about 3/32" above the surface of the fret board...
... and sand down to that as well. You want a slight angle down towards the peg head on the top surface. Also sand it to almost the finished width (same as the end of the fret board). Now gently place it in a vice and mark the slot locations on the top edge:
Then cut the preliminary slots with a "V" shaped needle file, taking care to always be cutting down at a slight angle towards the peg head. You want the strings to "break" right at the fret board side face of the nut, not up in the slot somewhere.
Check your progress with a thread stretched from the peg head back over the bridge. At this point, you want about 1/16" between the thread in the slot and the top of the first fret. (Later on, we'll take this down further...).
When all looks well, do the final shaping of the thing and glue it in place on the end of the fret board with just a little carpenter's glue. Slide back and forth to spread the glue and just let it set undisturbed (no need to clamp it).
Next: The saddle
If you find any of this helpful I'd certainly appreciate a "tip" :-)