I don't know about the airport transfers so you need to check with hotel. But remember you need to check the times of the shuttle bus in reception and book your seat for particular time. About metro, the shuttle bus will take you and collect you from the nearest metro station Comasina. You need to take yellow line to city centre. You can get out on Centrale FS or Duomo Station. There is small shopping centre beside the hotel where you can buy tickets or you can buy tickets in the machine in the station. Remember to follow signs for correct line by colour. You can download the metro map from Internet to have it handy on the phone. There is also bus stop beside hotel which will take you to red line metro station Sesto Maggio and you can get to Duomo from there. After firs time it's easy.