The fast train (TGV) leaves Paris from the Montparnasse station and goes to Vendôme, a 25 minute car ride from Trôo. Tickets cost from 25 - 45 euros each way, depending on the time of day. You can buy your tickets at the station, but it is cheaper to buy them in advance online, pay with your credit card, and then retrieve them at the station at an automated ticket machine using the same credit card. Visit the SNCF site, and from the drop-down menus choose "Paris Montparnasse 1-2" as the starting point, and "Vendôme Villiers-sur-Loir" as the end station.
You can rent a car from Avis and have it waiting for you at the TGV station in Vendôme Villiers-sur-Loir. Go to http://www.avis.fr to reserve.
If you want to rent a car from Paris, try Auto Europe and pick it up at the airport or in the center of Paris.
Note that bicycle touring is a wonderful way to explore the area. You can bring your bikes on the train and cycle to Trôo within a couple of hours.
To get to Trôo from Vendôme, follow signs for Montoire and then Trôo. It takes around 25 minutes. Parking for the Cave Yuccas is at the church at the top of the hill in Trôo. Coming from Vendôme, when you enter Trôo you should follow the main road along the river, despite signs you might see for the Cave Yuccas (the signs are posted for pedestrians). You will pass the bridge on the left and all the houses on the right, as if you are leaving the village. You drive down a long lane of trees bordering the road, and there will be a right-hand turn after the trees that will take you up to the village proper at the top of the hillside. Enter the village and straight ahead of you will be the church. Park on the right side of the church and descend by foot on the road past "La Butte" (the mound) and follow the little trail straight ahead that goes down to the cave houses. The Cave Yuccas is the second property to the right. NOTE: as there is no car access to the Cave Yuccas, you must be fit enough to walk on trails and climb stairs with your luggage, groceries from the market, bottles of wine, etc.
210 km (about 2 hours 30 mins) to Paris
122 km (about 1 hour 41 mins) to Chartres
121 km (about 1 hour 30 mins) to Orleans
53 km (about 1 hour) to Blois
48 km (about 51 mins) to Tours
66 km (about 1 hour 15 mins) to Le Mans
20 km (about 25 mins) to Vendôme