[hiccup]

You remove the wiring between the regulator and the alternator. From the factory this would have been a small (14AWG) blue wire and a small (14AWG) yellow wire. Sometimes there was temperature sensor installed on the alternator as well--this can be removed as it will no longer have any function. Essentially just connect the large ground conductor and large positive conductor to the new alternator.

The only other point to make is that some internally regulated alternators are not self-exciting. If your new alternator needs external excitation, this would be a new wire run from the ignition to the alternator (you could use the purple wire previously used to power the regulator). If you're not sure if the new alternator is externally excited, just try it without this connection, you won't hurt anything.