Getting to Montepulciano from Rome

You can take a train to Chianciano-Terme and then a bus or a taxi to Montepulciano.

Check www.trenitalia.com for train times. The bus runs roughly hourly.

The full train station name is Chiusi-Chianciano Terme. Buses to Montepulciano depart from in front of the station, usually just to the left as you exit. When I've taken the bus, the next departure was relatively soon after arrival by train. A taxi from Rome to Montepulciano would be extremely expensive, while the train/bus combination is rather inexpensive and pretty straight-forward. Ask your hotel which bus stop in Montepulciano to use. From the bus station (last stop), you may wish to consider a taxi as the uphill walk from there gets fairly steep.

To visit that area having a car is recommended.
If you are intimidated at the prospect of driving inside Rome, you can take a train to Chiusi-Chianciano T. and rent a car there. Chiusi is not far from Montepulciano and several rental agencies are present at Chiusi Scalo near the station (Europcar, Hertz, Avis).

We stayed just outside of Montepulciano and took the train from the above mentioned station to and from Rome. An easy trip but as Roberto suggested you will need a car to really enjoy the area around Montepulciano.