How do you know the alternator is bad? Usually the voltage regulator unit attached from behind the alternator is the culprit of insufficient charging. Pull the voltage regulator (2 Philips head screws) and check the contact brushes. If one or both aren't shiny, there isn't good contact with the armature.

To remove the belt - there is a bolt with a head and nut that take a 13mm socket. From the factory the bolt is nut to the front and head to the rear but it's often reinstalled the other way. There is a spring that holds the belt in tension. The bolt attaches to the top perch of the spring. The bolt is about 4" long and goes through the head casting. Remove the nut from the bolt, put a big screwdriver in the plastic upper spring perch, lever the perch CCW enough to remove the bolt, slowly release the perch. That will relieve enough tension to undo the belt from the alternator. If you don't have a belt routing diagram, draw the belt path for reference before you slacken the tensioner.

Sixto
93 300SD