Solution 1:

Swift 5.0 :

var dayComponent    = DateComponents()
dayComponent.day    = 1 // For removing one day (yesterday): -1
let theCalendar     = Calendar.current
let nextDate        = theCalendar.date(byAdding: dayComponent, to: Date())
print("nextDate : \(nextDate)")

Objective C :

NSDateComponents *dayComponent = [[NSDateComponents alloc] init];
dayComponent.day = 1;

NSCalendar *theCalendar = [NSCalendar currentCalendar];
NSDate *nextDate = [theCalendar dateByAddingComponents:dayComponent toDate:[NSDate date] options:0];

NSLog(@"nextDate: %@ ...", nextDate);

This should be self-explanatory.

Solution 2:

Since iOS 8 you can use NSCalendar.dateByAddingUnit

Example in Swift 1.x:

let today = NSDate()
let tomorrow = NSCalendar.currentCalendar()
    .dateByAddingUnit(
         .CalendarUnitDay, 
         value: 1, 
         toDate: today, 
         options: NSCalendarOptions(0)
    )

Swift 2.0:

let today = NSDate()
let tomorrow = NSCalendar.currentCalendar()
    .dateByAddingUnit(
        .Day, 
        value: 1, 
        toDate: today, 
        options: []
    )

Swift 3.0:

let today = Date()
let tomorrow = Calendar.current.date(byAdding: .day, value: 1, to: today)

Solution 3:

Updated for Swift 5

let today = Date()
let nextDate = Calendar.current.date(byAdding: .day, value: 1, to: today)

Objective C

 NSCalendar *gregorian = [[NSCalendar alloc] initWithCalendarIdentifier:NSGregorianCalendar];
 // now build a NSDate object for the next day
 NSDateComponents *offsetComponents = [[NSDateComponents alloc] init];
 [offsetComponents setDay:1];
 NSDate *nextDate = [gregorian dateByAddingComponents:offsetComponents toDate: [NSDate date] options:0];