At first, NSUserDefaults is a dictionary (NSDictionary I think). Every app has its own user defaults, so you cannot access the user defaults from any other app.
If the user (the one who plays your game) makes a new highscore, you have to save that highscore like this:
let highscore = 1000
let userDefaults = NSUserDefaults.standardUserDefaults()
userDefaults.setValue(highscore, forKey: "highscore")
userDefaults.synchronize() // don't forget this!!!!
Then, when you want to get the best highscore the user made, you have to “read” the highscore from the dictionary like this:
if let highscore = userDefaults.valueForKey("highscore") {
// do something here when a highscore exists
}
else {
// no highscore exists
}