If it's a Bosch unit, try tapping the regulator with the end of a screwdriver handle while the car is running and check your voltmeter.
If you get an incresaed reading, then simply replace the regulator/brush gear unit. It might be best to remove the alternator from the car as while the old part will come out easily because the brushes will be worn short, the hew piece will have to be carefully fitted by holding it at an angle to the back plate to allow the brushes to go in first then press it gently against the brush springs and make sure it's properly seated before refitting the mounting screws.
Splash out on a genuine Bosch unit if your local autoelectric shop has one as some of the spurious ones are simply crap.
You could also just replace the brushes if you're handy with a soldering iron but when you de-solder the leads, make sure the springs don't fly into oblivion and ensure you don't allow the solder to run too far along the wires when soldering the new brushes in as this can shorten the amount of travel on the brush.
Also check the condition of the sliprings on the end of the rotor shaft and if they seem grooved where the brushes make contact, it may be time to have the alternator rebuilt unless you feel confident to tackle it yourself.
It's not a difficult operation but if multiple problems exist with it, your heart will be broken before you're through.
