Yes—you can absolutely get usable aurora shots with a D3400. Start with your 18-55mm lens at its widest setting (18mm), since wide views are easier for aurora and night skies.

A simple approach:

• Put the camera on a sturdy tripod.
• Use a remote/shutter release if possible to reduce vibration.
• Set the lens/camera to manual focus and start near infinity; check test shots and fine-tune focus.
• Begin with a wide aperture (as open as your lens allows), ISO somewhere around 800–6400, and shutter speeds from a couple of seconds up to 30 seconds depending on brightness and movement.
• Take a test shot at high ISO first to check framing and focus, then adjust.

General tips:

• Compose first, then avoid bumping the camera.
• Wider apertures generally help capture more stars and light.
• If the aurora is moving quickly, use shorter exposures; if it’s dimmer and slower, try longer ones.
• Practice using your camera controls indoors before going out in the cold.
• Bring extra batteries and keep yourself warm.

Most importantly, experiment. Aurora conditions change fast, so expect to take many test shots and refine settings as you go.