A light NSDateFormatter subclass that's easy to use and understand. Though it probably won't work well with localization....

FLPRelativeDateFormatter.swift

import UIKit

class FLPRelativeDateFormatter: NSDateFormatter {
    static let sharedFormatter = FLPRelativeDateFormatter()
    override func stringFromDate(date: NSDate) -> String {
        let interval = date.timeIntervalSinceNow
        
        if (interval < 61){
            return "Just now"
        }else if(interval < 3600){
            let amount = Int((interval/60))
            return ("\(amount) minute"+((amount>1) ? "s" : "")+" ago")
        }else if(interval < 86400){
            let amount = Int((interval/3600))
            return ("\(amount) hour"+((amount>1) ? "s" : "")+" ago")
        }else if(interval < 604800){
            let amount = Int((interval/86400))
            return ("\(amount) day"+((amount>1) ? "s" : "")+" ago")
        }else {
            return super.stringFromDate(date)
        }
    }
}