A common NPN transistor (like a 2N2222 or PN2222) acts as a switch. The Arduino sends a "High" signal to the transistor's base through a 1k–4.7k ohm resistor, which then shorts the transmitter's key line to ground.
The K3NG keyer schematic is more of a "choose your own adventure" than a rigid blueprint. You can start with just an Arduino and a transistor and eventually scale up to a full-featured station controller with a display and memory buttons. k3ng keyer schematic