The way to create compelling, believable characters that will stick in your reader's minds long after the plot has faded into oblivion is to have something to say. If you have a compelling story, your characters will be compelling. You won't be able to help yourself. As cometh the hour, cometh the man, so too cometh the plot, cometh the characters. If your story is going right (and if you're honest with yourself), you'll see which characters are working, which aren't, and which should just be chucked in the bin.
That being said, that are things you can do to make handling your characters easier. Ask yourself, what sort of character does your story need? What is his purpose? How complex should he be. One complaint about many stories is that the characters are "wooden". This is a legitimate criticism and I've read many a story that felt like a trip to the lumber yard, but that isn't always the case. Some plots require very complex characters with deep inner lives and rich histories to make everything come alive. When we read something like Charles Dickens novel it's the characters we remember much more than this or that turn of the plot. Other stories, however, actually beg for a bit of termite fodder. Most science fiction, for example, leans very heavily on ideas and invoking a sense of wonder. More often what the author is interested in is what the character sees rather than who he is. A three-dimensional person becomes an actual liability in such a situation because he comes off rather like that twit who insists in standing smack in front of the Monet, so you can't get a decent view.
That said, it isn't an excuse for, as James Hilton wrote, creating a dummy and and hanging labels on it. I love the old Doc Savage novels with all their simple blood and thunder, but it amazes me how Kenneth Robeson (in his various incarnations) would time and again roll out some member of the cast who was little more than a few attitudes and adjectives–and I mean main characters. They weren't beloved characters; they were catch phrases and quirks wrapped up in descriptions.
Another thing to keep in mind is that the reader must care about your character. You may want to create the ultimate anti-hero, for example, but you can't make him utterly unsympathetic. You have to give the reader some reason to like him on some level and to root for him. Sure, he's a misogynistic, violent, unhygienic, uncouth cad, but maybe he's witty or smart or says things the reader would love to but never dares. Maybe he's the underdog. Maybe his enemy is infinitely worse by comparison. At any rate, your characters must appeal.
The same thing goes for sympathetic characters. Your heroine may be as lovable as the day is long, but don't assume that because she is lovable your readers will love her. Give them a reason; earn their affection. Show them why she is lovable by her words, her actions, and how other people react to her. If you borrow against what you assume is some demanded affection, then you're falling into mere sentimentality and manipulation.
But where do good characters come from? Ideally, they should spring from the plot and then the plot from them until an artistic Worm Oroboros appears, but there are other ways to get started. One of the simplest and easiest ways is to borrow from what you've read. By that I do not mean lifting characters whole from another work and passing them off as your own under a ginger wig and an assumed name. At best, you'll end up with a pastiche that is about as satisfying as a souffle reheated in the microwave or at worst, you'll descend into the artistic cul-de-sac of fan fiction and TV spin-off novels.
You can, however, use an existing character as a starting model for your own. that means taking traits or motives from various characters and recombining them to create something new. Maybe you want a character who's as charmingly befuddled as Father Brown, yet as coldly deadly as James Bond. Perhaps you want the insular romanticism of a Jane Austen protagonist mixed with the cosmic dread of a Lovecraft narrator. Maybe you want Conan the Barbarian via Bertie Wooster; there are all sorts of possibilities if you can piece the right parts together.
The most fruitful source for characters is real life. Many people believe that the talent of a writer is the ability to put words on paper. In fact, it's really the ability to observe and to shamelessly exploit what they've seen. Perhaps the best effort I've made at characterisation was a play I based on a collection of acting friends. If nothing else, it made the play very easy to cast. By taking the traits of my friends, exaggerating some, inverting others, and sometimes combining two people into one, I soon had a troupe of characters that were the most lifelike I'd ever managed. Curiously, when it came to actually producing the play the only character I had trouble with casting was the one based on me.
I wasn't at all suitable for the role.