There are several Internet cafes in town that charge $1/hour. Several coffee shops have Wi-Fi available with purchase of food or a beverage. Wireless Internet is available at the Hospitalito, free of charge.
Cell phones are sold in town for $20 or Q150. Local calls cost Q1 per minute; calls to the US are Q2 (25 cents) per minute.
US cell phones generally do not work in Guatemala. Check with your provider to see if you can purchase a special SIM card that will allow you to make calls within Guatemala, as well as international calls. There is a kiosk in the airport that offers SIM cards (next to the exchange kiosk).
Another inexpensive way to call other countries is through Skype or other Internet-based phone services.