How do I connect the HP DeskJet GT 5820 to a wireless network?

Ensure wireless is enabled on the printer — if the wireless indicator light is off, press the Wireless button to turn it on. Simultaneously press the Wireless button and the Information button to print a wireless network test report and network configuration page to diagnose connection issues. If the report shows the printer is not connected, press and hold the Information button for 3 seconds to print the wireless quick-start guide and follow its instructions. (Page 4)

From the official HP Impresora Todo EN Uno HP Deskjet GT Serie 5820 manual, page 4

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