Turin airport is only a 30 minute drive from the town centre. See the airport website for all departure/ connection options plus information on how to get to/ from the airport.
Milan is an easy train ride (approx. 2 hours) from Turin. Trenitalia has all timetable and ticket information. However, Milan has three airports: Malpensa, Linate and Bergamo, and the ease of travel to Turin from each varies greatly. Make sure you check the airport website and details of how to travel to Turin.
By rail you can connect to most of continental Europe. Check the Trenitalia website for all timetable and ticket information, and enjoy the ride!
Depending on how much time you have and how much scenery you want to take in, you can drive to Turin. Check friendly GoogleMaps for all of your journey options, but with the Alps & Switzerland to the north, the Ligurian sea & the rest of Italy to the south & East, and France to the west, you can have a very European adventure behind the wheel.
The Turin Planetarium is home to the first Astronomy, Astrophysics and Space Science centre in Italy. They have all the information you need about constellations, atmospheric patterns and places to park your space ship.
Turin is pretty well connected by Metro, bus and tram. The city transport website, GTT (gruppo torinese trasporti), is not the most user-friendly site but you can plan your journey and see the transport maps of the city. Aside from public transport there are bikes that you can hire, a high volume of taxis and, in the city centre at least, it’s very easy to get around by foot.
This Wikipedia page also has a lot of useful information about travel in and around Turin.