How to provide a localized description with an Error type in Swift?

As described in the Xcode 8 beta 6 release notes,

Swift-defined error types can provide localized error descriptions by adopting the new LocalizedError protocol.

In your case:

public enum MyError: Error {
    case customError
}

extension MyError: LocalizedError {
    public var errorDescription: String? {
        switch self {
        case .customError:
            return NSLocalizedString("A user-friendly description of the error.", comment: "My error")
        }
    }
}

let error: Error = MyError.customError
print(error.localizedDescription) // A user-friendly description of the error.

You can provide even more information if the error is converted
to NSError (which is always possible):

extension MyError : LocalizedError {
    public var errorDescription: String? {
        switch self {
        case .customError:
            return NSLocalizedString("I failed.", comment: "")
        }
    }
    public var failureReason: String? {
        switch self {
        case .customError:
            return NSLocalizedString("I don't know why.", comment: "")
        }
    }
    public var recoverySuggestion: String? {
        switch self {
        case .customError:
            return NSLocalizedString("Switch it off and on again.", comment: "")
        }
    }
}

let error = MyError.customError as NSError
print(error.localizedDescription)        // I failed.
print(error.localizedFailureReason)      // Optional("I don\'t know why.")
print(error.localizedRecoverySuggestion) // Optional("Switch it off and on again.")

By adopting the CustomNSError protocol the error can provide
a userInfo dictionary (and also a domain and code). Example:

extension MyError: CustomNSError {

    public static var errorDomain: String {
        return "myDomain"
    }

    public var errorCode: Int {
        switch self {
        case .customError:
            return 999
        }
    }

    public var errorUserInfo: [String : Any] {
        switch self {
        case .customError:
            return [ "line": 13]
        }
    }
}

let error = MyError.customError as NSError

if let line = error.userInfo["line"] as? Int {
    print("Error in line", line) // Error in line 13
}

print(error.code) // 999
print(error.domain) // myDomain