There are direct flights from the USA with most major US airlines. AeroMexico (www.aeromexico.com) and Interjet (www.interjet.com) fly direct from Mexico City. Avianca (www.avianca.com/gt) has flights to Guatemala City from most Central American capitals. If you are coming from elsewhere, you will almost certainly be changing planes in the USA, Mexico or elsewhere in Central America.
Guatemala City's Aeropuerto Internacional La Aurora (GUA) is the country's major international airport. The only other airport with international flights (from Belize City) is Flores (FRS). The Guatemalan 'national' airline, Avianca Guatemala, is actually a subsidiary of the Colombian company of the same name.
Guatemala levies a departure tax of US$30 on outbound air passengers, which should be included in your fare. If it's not, it has to be paid in cash US dollars or quetzals at the airline check-in desk.