Identify the wire at your HVAC equipment. A blue wire is often used for C. But you must confirm.
Power off your HVAC system at the breaker or main switch. Confirm it's off by trying to turn on heat or AC—no air should come from vents.
Remove your old thermostat. Carefully disconnect and label each wire using the provided labels. Label the wire coming from the wall, not any jumpers.
If you see a wire connected to a terminal labeled 'C' or 'COM' at your furnace or air handler control board, that's your C-wire. Connect it to the 'C' terminal on the ecobee backplate. You won't need the PEK adapter.
If that didn't work and there's no C terminal on your control board, you must use the included Power Extender Kit (PEK). Follow the wiring diagrams for installation without a C-wire. The PEK terminal on the Premium is labeled PEK+.
Heads up: The ecobee app has step-by-step videos and diagrams customized to your wiring. Use it. For safety, always shut off power before handling wires.