Your eyes and your camera disagree about what colour the aurora is, and both are telling the truth.
In low light human vision runs on rod cells, which are sensitive but cannot distinguish colour at all. So an ordinary display looks like a pale grey band that might be cloud until it starts to move. A sensor has no such limit: hold the shutter open for a few seconds and the green becomes obvious.
That gap is the single biggest source of disappointment on aurora trips, and it is entirely predictable. Knowing about it in advance turns a letdown into something closer to a magic trick, because you watch the grey band on the screen turn green.
Getting an image you will keep
Two routes, depending on what you brought.
What a phone can actually capture
Recent phones photograph the aurora perfectly well, held still. The tripod is not optional, and night mode is tuned for city streets rather than dark skies.
Camera settings that work in the cold
A starting point to dial in before you leave the hotel, and the rule most guides get wrong: shutter speed follows the aurora's movement, not its brightness.
The rule that matters most
Almost every guide says to lengthen the exposure when the display is faint. That is only half the story, and following it produces the flat green smears that fill photo sharing sites.
Match the shutter speed to how fast the aurora is moving. A quiet arc will take twenty seconds and reward you with detail. The same twenty seconds during a substorm, when the curtains are reorganising every second, averages all that structure into a uniform wash. The most exciting part of the night needs the shortest exposures.
Noise from a higher ISO is fixable afterwards. Motion blur is not.
If you would rather not bother
Perfectly reasonable, and about half the tours now include professional photographs for exactly this reason. The guide has shot the same scene several hundred times, knows the settings without experimenting, and can light you properly against the sky, which is the shot most people actually want and the hardest one to take yourself.
If you go that way, our page on tours with photos included covers what to establish first: how many images, what resolution, who holds the copyright, and when they arrive.