Most preferably you might want to use AVFoundation. 
It provides all the essentials for working with audiovisual media.
Update: Compatible with Swift 2, Swift 3 and Swift 4 as suggested by some of you in the comments.
Swift 2.3
import AVFoundation
var player: AVAudioPlayer?
func playSound() {
    let url = NSBundle.mainBundle().URLForResource("soundName", withExtension: "mp3")!
    do {
        player = try AVAudioPlayer(contentsOfURL: url)
        guard let player = player else { return }
        player.prepareToPlay()
        player.play()
    } catch let error as NSError {
        print(error.description)
    }
}
Swift 3
import AVFoundation
var player: AVAudioPlayer?
func playSound() {
    guard let url = Bundle.main.url(forResource: "soundName", withExtension: "mp3") else { return }
    do {
        try AVAudioSession.sharedInstance().setCategory(AVAudioSessionCategoryPlayback)
        try AVAudioSession.sharedInstance().setActive(true)
        let player = try AVAudioPlayer(contentsOf: url)
        player.play()
    } catch let error {
        print(error.localizedDescription)
    }
}
Swift 4 (iOS 13 compatible)
import AVFoundation
var player: AVAudioPlayer?
func playSound() {
    guard let url = Bundle.main.url(forResource: "soundName", withExtension: "mp3") else { return }
    do {
        try AVAudioSession.sharedInstance().setCategory(.playback, mode: .default)            
        try AVAudioSession.sharedInstance().setActive(true)
        /* The following line is required for the player to work on iOS 11. Change the file type accordingly*/
        player = try AVAudioPlayer(contentsOf: url, fileTypeHint: AVFileType.mp3.rawValue)
        /* iOS 10 and earlier require the following line:
        player = try AVAudioPlayer(contentsOf: url, fileTypeHint: AVFileTypeMPEGLayer3) */
        guard let player = player else { return }
        player.play()
    } catch let error {
        print(error.localizedDescription)
    }
}
Make sure to change the name of your tune as well as the extension.
The file needs to be properly imported (Project Build Phases > Copy Bundle Resources). You might want to place it in assets.xcassets for
  greater convenience.
For short sound files you might want to go for non-compressed audio formats such as .wav since they have the best quality and a low cpu impact. The higher disk-space consumption should not be a big deal for short sound files. The longer the files are, you might want to go for a compressed format such as .mp3 etc. pp.  Check the compatible audio formats of CoreAudio.
Fun-fact: There are neat little libraries which make playing sounds even easier. :) 
For example: SwiftySound