If you are driving: from Mexico City take the Mexico-Puebla highway (150) making the exit to Tlaxcala at the San Martin Texmelucan toll, pass the toll and drive with direction to Veracruz. Only 20 minutes latter you will find the detour to Tlaxcala.
If you are coming by bus: go to TAPO, Mexico City's East Bus Station and look for the bus line ATAH (Autotransportes Tlaxcala-Apizaco-Huamantla) the trip is around $150 pesos per person (subject to market changes) and it leaves every 15 minutes, with an ETA of 2:30 hours to Tlaxcala. You don't need reservations to travel.
If you are driving: from Puebla (Puebla) take the federal highway or the short road, both ways are easy to find and the roadside signaling is very clear.
If you are coming by bus: go to CAPU, Puebla's Bus Station and look for the bus line "Verdes" the trip is around 20 to 25 pesos per person with an ETA of 50 to 60 minutes to Tlaxcala.
If you are driving: from Pachuca (Hidalgo) take the Apan, Hidalgo highway. The road is pretty accessible and well paved. The ETA is about 50 minutes. If you want to take the non-toll road your ETA can be around 2 hours.
If you are coming by bus: from Pachuca's Bus Station, look for the bus line ATAH (Autotransportes Tlaxcala-Apizaco-Huamantla) or other bus lines which travel to the municipality of Apizaco and/ or Tlaxcala.