While undercover on the alien world of the Malcorians, Riker is seriously injured and rushed to a hospital where the Malcorian doctors discover his anatomy is nothing like theirs. "What are you?" they ask in astonishment. Riker attempts to maintain his cover by claiming he was born with numerous birth defects, but the Malcorian doctors are not persuaded. Could he be an alien from another world? The Malcorians are on the brink of warp space travel, but do not yet know that life exists elsewhere in the universe. Indeed, many in their society believe the universe revolves around Malcorian life. That belief may be about to change.
"First Contact" is one of TNG's underrated gems. It is actually about the very core of the Star Trek ideology: seeking out new life and new civilizations while observing the Prime Directive. It pursues these Trekkian themes using an approach that feels completely fresh and original. The episode's wisest choice is to tell the story primarily from the Malcorians' point of view; we come into the story with scarcely more information than they do, which means we, like they, must play catch-up. Aside from Riker, we see none of the Enterprise crew until the moment when Picard and Troi beam into a room with Mirasta (Carolyn Seymour), the Malcorian minister of science, to announce "first contact." Watching this happen through Mirasta's eyes is a crucial part of the effect; we're allowed to feel the disbelief, then fear, then astonishment, that she feels. It's like Picard and Troi truly are aliens from another planet.
Another reason this story is fascinating is that it shows us the nuts and bolts of how the Federation actually handles these delicate new encounters. Riker is just one of several other (unseen) undercover Starfleet officers who have observed and listened to Malcorian society for years in order to decide when might be the best time to initiate first contact. Riker going missing necessitated the process to be accelerated.
Next the Enterprise crew contacts the leader of Malcorian society, Durken (George Coe). Picard carefully tries to explain his intentions while putting Durken at ease, and in these scenes we get intriguing material that subtly reveals the apprehension both men feel in stepping wrong in these discussions. Durken suddenly realizes that he is but a speck of insignificance in the universe, and both Picard and Durken know that the Malcorians' fear might be viral.
Through Durken and his political administration we see the complexity of first contact in how it affects the society being contacted. It's possible — given the sociopolitical tendencies to maintain the status quo — that the Malcorians are not even ready to join the galaxy's community. Early scenes show more conservative elements, like Durken's security minister, Krola (Michael Ensign), expressing reservations over even the proposed warp flight, which didn't even assume that other life was out there. And there's talk about how Malcorian society should be taking care of itself before it starts going to other worlds. It's not often that TNG shows political details in a society that feel like they could plausibly come from our own current world, but these do.
Another detail I felt was important was how Picard puts the first-contact mission first, and only gradually moves toward the issue of getting Riker returned. This feels right; a Starfleet officer would put the diplomatic mission ahead of the man, especially with the stakes so high. Meanwhile, the hospital administration tries to keep a lid on the fact that they have a space visitor lying in one of their beds; they debate among themselves the implications of what they've got on their hands. When the lid does come off, there's a violent reaction and then political maneuvering by Krola to try to keep Durken from moving forward. Krola's maneuvering fails, up to a point.
In the end, a larger universe can't trump the societal status quo, and Durken declines Picard invitation, saying that his people aren't ready. Essentially it's a debate of progress versus what society will reasonably accept. "First Contact" has a lot of imaginative details about how this sort of encounter would play out using the Trek rules, and, for the most part, all the details feel right.