Usually you're attacked when other races view you as "hostile". You can change that by reducing the number of "-" or "--" in the foreign policy screen. Well, that's not always easy as outspoken because different races react *different* to the same matters, e.g. Drengin view a high diplomacy rating as negative while most others do not.

Best way to manipulate the relations is with Freighters. And also try to avoid some grave mistakes as positioning Military vessels (esp. Troop Transports) near enemy planets. Don't break treaties, and always help your allies.

If you go for Influence/Tech it would be a good idea to persuade your neighbours with all means into an alliance, probably sending all Freighters to one until he's allied, then re-routing the Freighters to the next.

Try to have a balanced/good military. However, if you are too strong it could be that several good AI's declare war unitedly upon you (probably a result of the Drath's SuperAbility)

Building Influencer Bases almost always give you a penalty or two - I'd do that only if I don't have to fear the AI (because he's too weak, or an ally). One problem is that during a war enemy planets don't flip.

There are actually alot of things you can do to better your diplo relations (e.g. gifting worthless Techs as Sensors) but you'll surely find out on your own over time.

I won a game that had Drengin in it on normal without having to build a single combat ship.  At the beginning I did try to expand as close to the Drengin as possible to deny them planets.  Since I wasn't researching military stuff I got a ton of Diplomacy tech and was able to have a great economy due to tech and low upkeep costs (no ships to pay for or maintain).  I made everyone like me and kept giving the Drengin money if they started to not like me.

At one point however I coerced the Drengin to attack one of my allies, forgetting that makes me obligated to declare war on the Drengin as well.  I was determined not to build any ships though, so I got all the planetary defense and soldiering tech I could, so Drengin were just running around with useless starships and were having a lot of difficulty actually taking out the planets since I would win the ground battles.

It was a fun game, but TBH I don't know if that strategy would have worked if Drengin had been more dominant in the galaxy.