I've been studying Spanish basically all of my life, but it's pretty safe to say that you don't learn words specific to different dialects in Spanish classes. Here are the top local words and phrases I had to learn and found useful during my time in Puebla:
Barbacoa: Specially cooked pork
Cemitas: Sandwiches with fried meat and (possibly) very spicy peppers
Chilaquiles: A breakfast dish of tortilla chips (and sometimes chicken) and a sauce made of either green or red peppers
Milanesa: Breaded meat fillets (any type of meat)
A la Parrilla: Charcoal grilled meat (any type of meat)
La Recta: An important highway that connects Cholula and Puebla
Sale: Okay
La UDLA: This is how taxi drivers referred to UDLAP
Zócalo: Town square
