outside the city but it is used only for helicopters and very small planes. The closest airport is the Veracruz international airport. It's about 2 hours from Xalapa.
By train
There are no passenger trains in 99% of Mexico since January of 2000. The only important exception is Chihuahua Pacifico betwen Chihuahua and Los Mochis.
By car
By bus
Almost-hourly buses go from Mexico City to Xalapa in several bus lines (ADO, AU), departing from TAPO station. The trip takes 4 hours approximately