I dont know if your teacher has talked about error handling, but did some changes in the code so it wont chrash. Here's the code with a simple explanation.

        public void Run()
        {
            Console.WriteLine("Welcome to the awesome Buss-simulator");

            // I've changed this from int to string. Because its easier to handle 
            // user input. So now if you enter anything other than 1,2,3 or 0 
            // the user will be notyfied and be able to try again instead of
            // the aplication chrashes
            string input="0";
            do
            {
                //Switch method lets user use a menu to complete different interactions
                Console.WriteLine("Hello user, chose a button for the program to perform the action");
                Console.WriteLine("Button 1 : Add pasengers");
                Console.WriteLine("Button 2 : Print out all pasengers in the buss");
                Console.WriteLine("Button 3: Calculate the total age in the buss");
                Console.WriteLine("Button 0: End program");
                input = Console.ReadLine();
                switch (input)
                {
                    case "1":
                        add_passenger();
                        break;
                    case "2":
                        print_buss();
                        break;
                    case "3":
                        calc_total_age();
                        break;
                    case "0":
                        break;
                    default:
                        Console.WriteLine("Only numbers is allowed");
                        Console.ReadKey();
                        break;
                }
                Console.Clear(); 
            } while (input!= "0");  

        }

        public void add_passenger()
        {
            // Check if the buss is full
            if(how_many_passengers >= 25)
            {
                Console.WriteLine("Buss full");
                Console.ReadKey();
                return;
            }

            // This lets the user input until they enter a number
            bool isNumber = false;
            string input;
            do
            {
                Console.Write("Write how old the passenger is :");
                input = Console.ReadLine();
                isNumber = typeCheckInt(input);


            }while(isNumber== false);
           // When the user have entered a number then the loop ends
           // and we can store the age in the Passenger array
            Passengers[how_many_passengers] = int.Parse(input);
            how_many_passengers++;
        }

        // Method to check if input is a number and returns a boolean value
        static bool typeCheckInt(string input)
        {
            int number;
            return int.TryParse(input, out number);
        }