You can add moves by talking to the Move Relearner, who is by the PokeMart in Mount Lanakila. Note, the Move Relearner can only teach moves that your Pokemon once knew (i.e. through forgotten Egg Moves or forgotten TM moves) or moves that it can learn sometime during level-up. There are also various move tutors around Alola that can teach your Pokemon specific moves, which you can view in the source.
You can delete moves by talking to the Move Deleter, who is by the PokeMart in Hau'oli City.
Hope I helped. :)