Are you needing directions to replace the whole alternator or the alternator pulley?
I believe you are referring to the belt tensioner. To remove it, first remove the belt, then remove the retaining bolt on the tensioner(see diagram below:
Here is a diagram of the belt routing so that you can make sure belt is on correctly:
Finally, make sure belt grooves are matched to all pulley grooves and not mis-grooved
Diagram showing what I mean by making sure grooves are matched(aligned) correctly:
The belt tensioner is worn out then and will need to be replaced.
Remove the belt, remove retaining bolt in belt tensioner to remove the tensioner. See 1st diagram in previous reply
Possibly coincidence, also possible that when belt was removed that tensioner was over-rotated causing it not to keep tension.