For Classics:
To remove the nut, firstly remove the truss rod cover and then lightly (really lightly) tap the nut with the wooden handle of a hammer (or a screwdriver) until the nut loosens and falls out.
Take the nut to Maestro at Pennisular and ask them for another nut of the same size, either TusQ or Graphite. The slots for the strings are already cut, so you only need to lower the nut until it is the same height as yours. The boys there can do it for you as you must be very careful not to round the base of the nut.
When you take the nut home, put some white wood glue in the nut slot and place the nut in the slot and restring the guitar. the strings will act as the clamp to hold the nut while the glue sets (normally overnight). clean up the glue with a damp cloth, make sure the nut is sitting properly and you're done.
It won't be the most professional job you can get, but at least you did it yourself.
cheers,
Mark.