This is probably your easiest way to get to Alessandria. If you can, we advise you to have your flight arrive in Torino ("Turin" in English) as opposed to Milano as there is a direct train to Alessandria from the train station in Torino.
At the airport, it is possible to take buses to Porta Nuova train station (the main train station in Torino). The bus is called SADEM and it departs about every 15 minutes. This trip is about 45 minutes long and you can buy tickets on board (it will cost 5, 50 euros)
From the train station of Porta Nuova you need to take a train whose destination will be listed as one of the following: Bologna, Genova or Reggio Calabria.
Alessandria is about one hour by train from Torino.
