I have come across an NPR but all that happened was I initiated communications, and every once in a while I see a ship fly by. I haven't found any of their planets yet so I can't attack them (I wouldn't want to anyway), and I figured there wasn't any real diplomacy since nothing diplomatic has happened. I did ask about what you can do with aliens and how to do it in the "Alien Contact!" thread but nobody ever responded.
Well, no expert on diplomacy with aliens here, but a few points I gathered.
1. You should form a diplomatic team for any alien race you encounter, if you want to play peacefull. This will, over time, improve you standing with that race
2. Once your standing gets good enough, a couple of options (sharing geo and grav survey data, sharing research, sharing jumpship use,...) become possible (look at the diplo screen (Ctrl+F5). For some options to become possible you need very high postive ratings, which will take quite some time, even if you do nothing stupid, to lower them (like, putting a battlefleet in orbit over their homeworld, for example)
3. Best look at this post from Steve, where he explains how diplomacy from 4.1 on is working
viewtopic.php?f=1&t=1613&hilit=diplomacy#p14676