There's a great philosophy podcast called the Partially Examined Life, they did a two part episode on this book a while ago. They usually do a pretty good deep dive into things. Hope this helps!
What point did you make of it? If you don't tell your conclusions there is no way to know if you missed the point.
Its full of ugly, vile characters (and so is every Dostoyesvky book), and tense situations. The big pciture of the book is the contrast of Michkin's actions in relations to everybody else. This contrast is were the message lies, trying to be good in a world lead by "evil" motivations can only guide you to madness.
Dostoyevsky is notorious for his style of writing, where no character really *speaks* for the author. It's not like Myshkin is the perfect person, and everyone should just be like him. He's very inconsiderate when you think about, in the way that his lack of ability to adjust his behaviour makes him a catalyst for all sorts of bad things. He's a Christ-like figure, Dostoyevsky describes him as the most beautiful person, but beauty doesn't thrive in the real world. None of the characters are clear cut, they're unpredictable and intensely human, which is the amazing and frustrating thing about reading Dostoyevsky. Don't feel bad if you feel like you missed some deep moral of the story, there isn't really any monolithic message.
EDIT: I also strongly recommend listening to the episodes Partially Examined Life dedicated to the book, great informative and funny listening.
As someone below said, Welcome to Russian literature. I know quite a few Russian speakers who have the added benefit of an intimate knowledge of the language and culture who are left puzzled by the writings of Dostoevsky. I'll just say you haven't experienced the true bewilderment one gets on reading Crime and Punishment.
Anyway, The Idiot is a daunting task, both to read and to understand. You must realise that Dostoevsky is a philosopher. While he might not write philosophical treatises, he does incorporate certain subjects into his writing. The good news is that The Idiot is largely devoid of these philosophical points (as far as I can tell. If anyone can refute me then please do). The bad news is that The Idiot is a largely spiritual work, one which deals with the state of the Russian man.
Dostoevsky, as far as I know, was not affiliated with the Slavophile movement. He did, however, share many ideological views with them. Just to quickly say that the Slavophile moment was a 19th century intellectual movement born out of a contempt for the Westernisation Russia underwent during the reigns of Catherine the Great and Peter the Great. Many saw the decline of Russian values, which were perceived as unique, as a threat to Russia itself, and proposed modelling Russia on traditional Orthodox values (many valued the church above the state) and trying to restore Russia to it's glorified past.
And this is largely the basis of the book. It tries to examine the spiritual conflict taking place within Russia during the 19th century. The characters within the book are, by and large, terrible people. They're schemers, or damaged or outright rogues. There's one shining example of a good character, one who's used as a contrast to this 'degradation', and that's The Prince. Dostoevsky wanted to see what would happen if the purest man were to be placed in this network of bad people. Bearing in mind that D was a devout Christian, who is the purest man that could be thought up? Of course the answer is Christ himself.
So that's what the book is. It's examining the spiritual state of the Russian man during the processes of increased Westernisation during the 19th century. I'm not surprised if you feel somewhat disturbed by the book's conclusion. There is no redemption in the end. The degraded Russian spirit, owing to increased European influence, destroyed Christ, and this influence was only increasing in Dostoevsky's mind (you might recall the closing paragraph where Lizaveta Prokovfyevna comments on the railways going evermore East and ominously encroaching on Russia).
This is the main point of the book, in my mind at least. There are other conclusions I've drawn from reading the book, but there is not the space here to adequately detail it. So I'll leave it here.
Read twice. Yeah, not much to add here. His characters are a bit sticky and can linger on the periphery for a bit.