International flights arrive at Tocumen International Airport (PTY) in Panama City. Services arrive daily from the US (most are routed through Atlanta, Dallas/Fort Worth, Houston or Miami) and other Central and South American cities; KLM and Iberia fly from Amsterdam and Madrid, respectively. Flights from San José, in neighbouring Costa Rica, often stop in David before continuing on to Panama City. The recently upgraded airport in David is expected to see direct international flights from and to the US at some point.
You can cross into Panama by land from Costa Rica, but due to security concerns it’s not possible to do so from Colombia. Instead, backpackers are increasingly booking passages by boat.