One of the biggest problems with characterization is the fact that a character – one written down – is frozen in time and space. Once you have had them react in a situation, every time the reader comes back to reread that scene, that character is always going to react the same way. No surprises. This is an inescapable flaw built into the medium of the written text. So how can a writer overcome this?
One of the best methods is to hint at a character’s emotional uncertainly or ambiguity of her or his motivations. The character of Grace in Margaret Atwood’s Alias Grace is an excellent example of this technique. We never really know if Grace Marks was a participant of the novel’s central crime or just another victim of the horrific circumstances. The ambiguity complicates the character of Grace, hinting at fleeting depths that the reader can only glimpse. Most of the heavy lifting of the characterization is done in the imagination of the reader, because Atwood never comes straight to the point as she crafts the Grace character. There is no resolution to this ambiguity, and so the reader is left to ponder.
Another method is to construct an elaborate setting and history (or background) that allows for the character to have a life ‘outside’ of the events of the narrative. Terry Pratchett’s Discworld is the best example of this I can think of, with Discworld providing a broad range of 3D characters that often interact with each other while wandering through the increasingly complicated landscapes and cities. This worked so well for Pratchett that even throwaway characters ended up with books of their own, such as The Amazing Maurice and his Educated Rodents. This is a lot of work for a writer, but it has the benefit of creating a worldscape you can visit again and again without getting boring. Other examples would be Tolkien’s Middle-earth and C S Lewis’s Narnia, and a Steampunk genre example would be Stephen Hunt’s the Kingdom of Jackals.
You can also base a character on a real life historical personage, like Grace from Alias Grace. Your character then comes with a ready-made background and setting, maybe even a plot. The drawbacks of this technique is that you are also limited by the reality of that personage, and you need to do a lot of research. Unless you’re playing it for laughs, the elderly Queen Victoria was not a secret ninja fighting against an invading horde of raygun-wielding goblins (though I wouldn’t mind reading a book like that, to be honest). In her later years, she was reclusive and depressed, and sought only the company of her family and trusted companions, which only makes her a better inspiration for a character, to my mind, because we tend to think of queens as powerful. Using Queen Victoria as inspiration also means you have a lot of information to deepen and add details to a characterization.
These aren’t the only techniques you can use, but these are the three I find the most helpful.