SWIFT: How do I add hours to NSDate object

Use NSCalendarComponents:

let calendar = NSCalendar.currentCalendar()
let newDate = calendar.dateByAddingUnit(
    .CalendarUnitHour, // adding hours
    value: 2, // adding two hours
    toDate: oldDate,
    options: .allZeros
)

Using NSCalendar will account for things like leap seconds, leap hours, etc.

But as Duncan C's answer points out, simply adding hours is definitely the wrong approach. Two time zones won't always be separated by the same amount of time. Again, this is something especially true when we take daylight savings into account. (For example, the United States doesn't start/end daylight savings on the same days as Europe, and Arizona doesn't even do daylight savings).

You're asking the wrong question. This is what's known as an "XY Problem". You should be asking "How do I display a date string I get from a web server in the user's local time zone."

NSDate represents a date/time in an abstract form that does not contain a time zone. You convert it to a specific time zone for display. Do not try to add/subtract hours to an NSDate to offset for time zones. That is the wrong approach.

The correct answer is simple. Create a second date formatter and don't set it's timezone to GMT. It defaults to the user's local time zone.

let dateFormatter = NSDateFormatter()
dateFormatter.dateFormat = "yyyy-MM-dd HH:mm:ss"
dateFormatter.timeZone = NSTimeZone(abbreviation: "GMT")
let date = dateFormatter.dateFromString(dateFromService) 

let outputDatedateFormatter = NSDateFormatter()
outputDatedateFormatter.dateFormat = "yyyy-MM-dd HH:mm:ss"
//leave the time zone at the default (user's time zone)
let displayString = outputDateFormatter.stringFromDate(date)
println("Date in local time zone = \(displayString)")