Use some thin hardwood wood veneer so the thickness will be consistent. You may be able to pick some scrap up from a local cabinet shop or find small pieces at a home supply store.
Cut it to size with an X-acto knife and a straight edge. From what you describe it may take more than one layer. Cut the piece(s), dry fit and tune to pitch and play it first to see if the height is high enough so the strings don't buzz on the 1st fret. If the nut is a little high, that's alright it'll be taken care of later. If the nuts too low, add another shim.
If everything is OK or slightly too high, glue the shim(s) to the fret board with Elmer's glue. Do not glue the nut yet. Use the nut and some string tension to clamp the shim(s) while the glue dries.
If the nut height is a little high, use a flat file or sand paper on a flat block and remove material from the shims slowly. Check the nut height often. It's easy to take off too much. When you think you can take a little more off so it will be perfect, STOP.
If you have a rosewood board use a Sharpie or Magic Marker to color the shim.
Use a drop of the Elmer's to lightly glue the nut in place using string tension to clamp it.
Make sure the nut is centered. Use string tension on the outside strings to adjust the centering of the nut while the glue is drying. The strings don't need to be tuned to pitch, just tight enough to hold the nut in place.
mech
