Getting factions happy

Kill the opposing faction enemies.

for confed, kill retro, pirate and kilrathi.
For merchants and militia, kill pirates and I think also retros.
Hunters kill kilrathi
for kilrathi kill confed.
for pirates, kill merchants
I don't think you can get good retro relations

this list is by no means complete, but this is what I remember off the top of my head. It should at least get you started