every time you do something that benefits a faction, you'll see a small blue arrowhead pointing up beside their entry in the right hand panel's faction page
- deliver their cargo, trade with their station, sell them exploration data, kill their enemies, help their friends etc.
likewise if you do something they don't like, you'll see a red one pointing down
- kill their ships, help their enemies, fail their missions etc.
-- Fly safely, shoot straight, kill quickly, land softly --