While watching the northern lights in Norway and Sweden in 2016 & 2017 (see my travel post), I managed to take some nice photos of the spectacle. Of course there is room for improvement, so let me share the insights from my first go at it.
Lady aurora putting on a show over a lake in Sweden (7-14mm @7mm, 30s, f4, iso 1600).
Starting with the gear. I have a micro 4/3 camera that I got mostly to take video and photos underwater. It is not the ideal set-up for astrophotography. Compared to the GH4 (see my gear post), other cameras with a larger sensor and higher light sensitivity would be better, but then again there is always a better set of equipment out there.
Time-lapse of the northern lights taken in Andenes.
For the lenses, it is all about speed and field of view. On my first trip north, I had my 7-14mm wide-angle lens (great for photos of sharks) which covers a relatively large portion of the sky, but is slow at f4. Then I also have a 25mm with a limited field of view but a fast f1.4 aperture. When the aurora was strong, the f4 lens worked ok and for time-lapses the faster lens allowed taking a shot every 3 seconds to get a smooth transition between frames. The time-lapse above was shot mainly with the 25mm lens. You can see the section shot at 7mm where the frames “jump” more because of slower shutter speeds and associated processing time between shots. 
The northern lights above a snowy field (8mm, 30s, f2, iso 1000).
On my second trip, I borrowed Simon‘s 8mm fisheye lense with a fast aperture, and it made a huge difference. The wider aperture brings in more light, so you can have a faster shutter and more defined auroras, and the wider angle allows you to capture more of the sky. If I end up doing more night photography, I’d definitely get that fisheye lens.
The northern lights dance above Andene’s lighthouse (8mm, 2s, f2, iso 1000).
Apart from that you need a tripod and use the 2 second timed-release function so you don’t blur the photo when pressing down the shutter button. Carry a spare battery with you as well, as they run out faster at -30°C. The last thing concerns the infinity focus. In a dark night and without a light-up object close by you will have to manually focus. I realised that simply focussing all the way to infinity doesn’t produce sharp photos after an amazing aurora show…so don’t make the same mistake and learn first where the infinity focus of your camera and lens actually is.
This could have been a pretty photo, if I had manually focused correctly… (7-14mm @7mm, 10s, f4, iso 800).
When the northern lights are dancing fast, a 2 sec exposure at f2 should about do, otherwise you start losing the structural detail and the beautiful lights become a big green smudge on your photo. So in dark nights, a more relaxed aurora can be better because you can leave the shutter open for 20 or 30 sec and also get a bit of light on the mountains and some stars in the sky. Generally, you’d want to avoid overexposing the aurora because pulling down the highlights during processing can only do so much, while there is more wiggle room with brightening the dark areas. Finally, in post you could of course play with the colours, and the colours of the aurora do vary depending on the strength. I tend to not adjust the colours, and my aurora experiences were often quite green, but we also had some lovely turquoise and purple.
Another great aurora dance on a cloudy night (8mm, 2s, f1.8, iso 1000).
One of my favourite shots took a little bit of editing to get the complete heart shape. I darkened the top right corner of the heart, and I reckon the result is worth the tinkering 🙂
The northern lights produced (almost) a heart shape. Full disclosure: I dropped the exposure by -1.6 around the top of the light in post …(7-14mm @ 7mm, 13s, f4, iso1000).
Once the technical things are mastered, we can think about image composition. There are some great shots out there of a reindeer with the aurora in the back, or amazing reflections in an ice-berg filled lagoon. Staying in the same place for a few nights can help with composing a good shot since you can anticipate where the aurora likely shows up. Having said that, I composed my 8h time-lapse after 3 nights of observing the aurora and she ended up mostly dancing just a bit to the right that night 🙂