How do I put objects in an NSArray into an NSSet?

This is not correct:

NSSet *telephoneSet = [[NSSet alloc] init];
[telephoneSet setByAddingObjectsFromArray:telephoneArray];

That method returns an NSSet which you are doing nothing with (it doesn't add the objects to telephoneSet, it creates a new NSSet). Do this instead:

NSSet *telephoneSet = [NSSet setWithArray:telephoneArray]

Also, note that a set cannot contain duplicates unlike an array. So if you have duplicate objects in your array and you put them in a set, the duplicates will be removed which can affect the object count.

Initially telephoneArray contains references to n distinct objects. After the loop ends, it does contain n references, but each one is pointing to the same newTelephone object.

Array can contain duplicates, so it doesn't matter. A Set cannot have duplicates, and your entire telephoneArray is composed of a single object basically, so you're seeing just one.

In your loop, you have to create a new object or get a telephone object from somewhere:

for (int i=0; i<[telephoneArray count]; i++) {
    // Create the new object first, or get it from somewhere.
    Telephone *newTelephone = [[Telephone alloc] init];
    [newTelephone setBranch:newBranch];
    [newTelephone setNumber:[[telephoneArray objectAtIndex:i] valueForKey:@"number"]];
    [telephoneArray replaceObjectAtIndex:i withObject:newTelephone];
    // the array holds a reference, so you could let go of newTelephone
    [newTelephone release];
}

Also, like PCWiz said, you don't need to allocate a new NSSet object in your case. Just call the class method setWithArray:.

NSSet *telephoneSet = [NSSet setWithArray:telephoneArray]

Swift 3 Version

You can create a new NSSet from an array with:

let mySet = NSSet(array : myArray)

Additionally, you can add objects from an array to an already existing NSMutableSet with.

myMutableSet =  myMutableSet.addingObjects(from: myArray)