Shapes are mostly determined by the strength and speed of the solar wind. Depending where you are to view auroras, some shapes will be more common than others. Let’s go through some of the common shapes, starting with the relatively calm ones, arcs, high needles and curtains.
Weak solar wind might create ‘only’ a very pale, green ‘fog’ or low arc on the horizon which -to the eye – barely moves at all. With speed and strength picking up, that arc comes to life and moves faster. It can turn into a curtain with needles rising high up in the sky. I like to call this a curtain because it reminds me of a stage curtain in a theater. Usually I imagine someone is at one end of that curtain moving it back and forth creating waves. During stronger nights there are multiple arcs spread over the sky.

350° Aurora borealis
Auroras above the frozen Sea

Let’s go to the crazy stuff like spirals, coronas and flickering
Spirals travel from the low horizon upwards and dance in curves. This is often happening with strong solar wind. If this happens relatively high, you will start to see countless needles rushing through. Once right above, a corona will most likely open up. Countless rays spread out in multiple colors. This usually lasts only for a short time as the aurora moves on. Towards the end of the night, there is often a kind of flickering, where parts of the sky above are randomly lit up by weak auroras and switched off within split-seconds.

Usually a mix of these shapes will appear in the sky, including shapes that were not described here. As with nearly everything aurora-related, every night can be different.