A woman walks into the office of Spade and Archer, asking them to tail a man for her. Archer does the tailing, and somebody shoots him. When the man he was tailing turns up dead too, the police suspect Sam Spade of doing it to avenge his partner. When they find out that Spade was having an affair with his partner's wife, they suspect him of that crime too, even though it sort of cancels out the other motive. Meanwhile, the woman who hired him wants his help with something that she won't actually explain or even give a decent hint about. Then, Peter Lorre shows up in Spade's office with a gun, asking about a bird statue.
Don't get me wrong, I don't have anything against detective movies. If I did, I never would have rented this thing. The Big Sleep is a great example of how something like this can actually work. The Maltese Falcon, though, is a perfect example of almost everything that's wrong with detective movies.
Humphrey Bogart was a good actor, but this is not some of his better work. With the exception of Lorre, the supporting actors are uniformly boring. The script isn't exactly thrilling, either.
I kind of like the ending, though.