How do they work?

I've only had about three hours to fiddle around with the game and... ugh... I'm really underwhelmed. No where I go seems to have any sort of coordination or control. Every instance has a ton of random ships thrown into it, there's almost no way to reach the anomalies, and in the 12 instances I've run so far I see others getting drops regularly (white pylons) but I've gotten... none.

So, is there some magic formula to get drops?

I guess it is who causes the most damage to the ship before it gets killed?

If you're not teamed with others, whoever does the most damage to an enemy gets the loot. Does not matter who gets the first shot in.

If you are teamed with the others, it depends on the loot rules the leader set.

Check under Social what your group loot settings are. Some group leaders are setting 'Master Looter', which means the team leader gets all the loot.

So, pure aggression gets all the loot.
If you tank you loose?

Nope, if you're grouped in an instance it's up to the group leader. They can set it to round robin if they want....or don't.

Only if you are NOT teamed.

Maybe they should change the "open teaming" to automatically go to round robin or most damage etc.....

It is kinda worrying that the group leader gets to choose especially since you can fly into a mission and be grouped automatically.

It does default to Round Robin with "open teaming"

However, the leader can change that Round Robin to something else, or even change the default setting for Open Teams when he is the leader via the social menu.

Just turn grouping off.