Um. Read the messages. The AI itself will tell you how to impress it - it depends on the Trait it's using at the moment. Some AI will be impressed just because you're producing incredible amounts of food. Yes, that happens. In one of my recent Soyuz games, multiple people loved me because I had a massive, advanced military (Respect, not Fear). Daoming, Hughes, and Elodie were sniffing the gunpowder big time.
Bigger doesn't always mean more respect. In my current game, I have a massive empire, but Fielding won't give me the time of day because my spy network is crap. Good thing her Fear is way up. That won't always work, though. Kolzov attacked me at 9 Fear, 0 Respect. Something about having enough of cowering under the big bully. Yes, the diplo message actually said that.