If you arrive in Puebla at CAPU, we recommend that you take a "taxi autorizado" to INAOE, which has a regulated price. There are several kiosks inside CAPU to buy the tickets to these taxis, all labeled "taxis autorizados". The nearest kiosk is inside the station, at the arrival launge of the Estrella Roja bus. The ticket to Tonantzintla is $163 to $169, depending on the hour you take the taxi, and the ride takes about 30 minutes. Inform the driver that you wish to go to "El Observatorio" in Tonantzintla.
If you arrive at 4 Poniente, there are only standard (black) taxis. You need to negociate the price with the driver before you get into the taxi. The taxi should cost $200 MXN or less.
If you arrive at the Huejotzingo-Puebla Airport, you will also need to take a taxi autorizado, with a regulated price.
If you are more for the adventure, from CAPU terminal there is a red bus which is label "Chipilo" through Momoxpan and Tonantzintla. It leaves from the previous to last rail every 30-45 min and it says "INAOE" on the front. It costs $7.50 MXN and takes around 1:15 to 1:30 hours, you should ask for the INAOE stop after leaving Cholula.