Where should I fly to?

Flying to Turin:

From the UK it's possible to fly to Torino Caselle, which has direct flights from London Gatwick (British Airways), London Stanstead (RyanAir) and Edinburgh (Jet2, RyanAir, easyJet).

If you're flying from further afield, you can either fly to Milan and take a train onwards, or it should be simple to fly to any major EU hub (Amsterdam, Paris CDG, Munich, Frankfurt, Rome) and get a connecting flight to Turin.

Flying to Milan:

Milan has 3 major airports, Linate (east side of Milan) & Malpensa (west side of Milan) & Orio al Serio (located in Bergamo, to the north east of Milan). It's fairly simple to arrive from any of these into Turin using public transport, see below for details.

How do I get to Turin from Milan?

Transport to Turin from Milan Orio al Serio (Bergamo)

Milano Bergamo is a medium-sized RyanAir hub just outside of Milan. To travel onwards to Turin, take any of the buses immediately outside the front door of arrivals to Milano Centrale (the railway station, ~50mins, ~€12). Buses leave every 15minutes or so throughout the day.

Once arrived at Milano Centrale, simply walk inside and buy a ticket to Torino Porta Nuova from any of the ticket booths available. There are 2 train companies (Italo & Trenitalia), and a high-speed train will cost ~€35 and will take ~1 hour.

Transport to Turin from Milan Linate

A tube line from Milano Linate will take you to Milano Centrale Railway Station. From here, take a train to Torino Porta Nuova as above.

Transport to Turin from Milan Malpensa

Bus:
The best way onwards from Milan Malpensa is to take one of the airport buses direct from the airport to Torino Porta Susa. These take ~2 hours and cost ~€22 per person.

Train:
Alternatively, you could take a bus from Milan Malpensa to Milano Centrale Railway Station, and catch the train to Torino Porta Nuova as above.