Hi I'm traveling from Milan airport to Rome in September. Then, Rome to bellagio. I'm not sure when I should purchase a high speed train. Should I buy it at the train station? Does the kiosk ticket machine have high speed train? Or should I buy it a month before my trip? Please help.

Do you know about the maninseat61.com - the resource for all things train related.

buy up to 3 months before at www.trenitalia.com or www.italotreno.com-- two separate high-speed train operators.

Rome to Bellagio - Rome to Milan then regional train Milan - Varenna-Esino -then ferry to Bellagio.

Yes www.seat61.com has lots of tips on booking your own online - the best site for that. For general info Italian trains - www.ricksteves.com and also www.budgeteuropetravel.com.

check first class too as sometimes it may not be much more than the cheapest remaining second class seats and if not much more go in a bit more relaxed style -2nd class is fine but 1stcl finer.

The general wisdom is to buy them as soon as they go on sale for the best discounts. Refer to the website link above for the dates.

I refer to the seat61.com site for the most comprehensive information.

The cheapest tickets you buy months in advance are non-refundable. If you flight arrives late and you miss the train, you're out of luck.

The walk-up tickets you buy on the day of arrival will be fully flexible but most expensive.

As early as possible if you believe that your plans will not change, the flight will be on time, your luggage will make it, and you like or can plan your days to a minute months in advance.

Leave lots of time between plane and non-refundable train ticket time -well worth the wait - see what difference between discounted ticket and full fare- may not be much or could be then decide.

Thank you all!!

Do I take a train from mxp airport to get to Milano centrale?

Yes.

I like this site for various transport options between 2 points. Some here complain that it isn't infallible but what is? https://www.rome2rio.com

Google maps will find TrenItalia routes and schedules. It's better then Rio. Google won't find Italo but much of the OP routing requires TrenItalia

Do I take a train from mxp airport to get to Milano centrale?>

Yes but there are two Malpensa airport trains -one goes to Milan Cordona station near the town center so be sure you take the one to Milan Centrale.

Thank you everyone!!