The thing about Neruomancer and Gibson's writing in general is that it's so linguistically dense. In the first two chapters of the book (Chiba City Blues) we're introduced to a number of characters, all of whom are brought to life in a few very descriptive lines.
Case, the main protagonist, is a former cyberspace cowboy who skimmed from a former employer, who then destroyed his nervous system making it impossible to jack into the net. Since then he's been working in the Chiba prefecture in an area called Night City *ahem* as a fence and deal broker. He's desperate to get fixed and back to the net, but it hasn't been working and now he's on a singular path to self destruction.
Ratz is the owner of the Chat (Chatsubo) Case's local and is a former soldier and Gibson makes a point in describing his rough Eastern European prosthetics, so already we can infer something about the past and character of Ratz. Ratz lets Case know that Wade, the man Case deals with, is looking to have Case killed because of some debt, so we know Ratz has a soft spot for Case.
We also learn about Case's former girlfriend, Linda Lee. She fits the typical nihilistic punk girl of the early 80s, but she's also a drug addict. While they enjoy each other's company for a while, neither Case nor Linda are very attached to the other.
And then there's Molly. Case is paranoid enough already, but his use of 'dex' (possibly a derivative of dextromethorphan), make him even more so. When Case discovers he is being followed he bolts and through a short chase we glimpse Molly with her chrome covered eyes and her deadly skills.
Gibson, in introducing us to the characters and the world they live in, also creates what is essentially a new language. This is one of the key complaints many first time reads of Gibson have. Gibson doesn't hold your hand or help you along. You either 'get it' and get if fast, or you don't. If you don't you're left far behind and bewildered and he doesn't care. He just keeps the prose and the new language going. It's a lot like being dumped in a country where you don't speak the language and left to either find a way to get yourself understood. Or not. I've often said Gibson was more half a linguist than an author.
I can tell you, that reading this for the first time in 1984, was a revelation. It spoke to the heart of the social and political climate of the time with Thatcherism and Reaganism and the way big companies were really starting to take over. It was also the year that Apple introduced the Macintosh, which was a huge leap for computing ease for the average user.
For me, Neuromancer hit all the right buttons at the right time. After years of reading about clean spaceships and super advanced technology that was wonderful, here was a story set in a reality I could see happening. I could feel it as a real possibility. It was a scary possibility, sure, but if you had enough guts and enough brains and enough luck, you could find a place in it. And that was rather comforting.