how to use Alamofire with custom headers

According to the official documentation, modifying the session configuration is not recommended:

This is not recommended for Authorization or Content-Type headers.
Instead, use URLRequestConvertible and ParameterEncoding,
respectively.

So an example usage of URLRequestConvertible for authorization would be:

enum Router: URLRequestConvertible {
    static let baseUrlString = "some url string"

    case Get(query: String)

    var URLRequest: NSMutableURLRequest {
        let (path: String, parameters: [String: AnyObject]?) = {
            switch self {
            case .Get(let query):
                return ("/get", ["q": query])
            }
        }()

        let URL = NSURL(string: Router.baseUrlString)!
        let URLRequest = NSMutableURLRequest(URL: URL.URLByAppendingPathComponent(path))
        // set header fields
        URLRequest.setValue("a", forHTTPHeaderField: "Authorization")

        let encoding = Alamofire.ParameterEncoding.URL        
        return encoding.encode(URLRequest, parameters: parameters).0
    }
}

and when you want to make a request:

Manager.sharedInstance.request(Router.Get(query: "test"))

More info about URLRequestConvertible: https://github.com/Alamofire/Alamofire#urlrequestconvertible

Old Answer

As of Alamofire v1.0 Pers answer no longer works. In the new version additional headers should be added to the HTTPAdditionalHeaders property of NSURLSessionConfiguration

Alamofire.Manager.sharedInstance.session.configuration.HTTPAdditionalHeaders = ["Authorization": authorizationToken]

More info here: https://github.com/Alamofire/Alamofire/issues/111