Uber is by far the most practical way to get around Guatemala City. It is safe, air-conditioned, and the app shows you the fare before you commit. Street taxis exist but should be avoided — there have been incidents of taxi fraud and express kidnappings in unofficial cabs. Only use taxis from established stands at hotels or the airport.
The Transmetro is Guatemala City's bus rapid transit system, running along dedicated lanes on the main avenues. It is cheap, efficient, and reasonably safe during the day, though it gets very crowded at rush hour. Routes connect Zona 1 with Zonas 4, 9, 10, and 12. The Transurbano bus network covers more of the city but is slower and harder to navigate without local knowledge.
Walking is fine within Zones 9 and 10 (the modern zones), and within the central blocks of Zona 1 around the Plaza de la Constitución and the historic sights. Avoid walking in Zona 1 after dark, and be cautious around the bus terminals in Zonas 4 and 12 at any time.