In general, I don't have a specific method; I just ponder until I find a name that feels right, whether because of meaning, or association with someone I know in real life, or just a name I like that seems to "fit" the character. Sometimes I don't get it right at first and I'll think of a better name later on. I do find, though, that after a certain point in the creative process, when I've thought of a character with a certain name for long enough, that becomes their name and I can't think about changing it any more.
For my current RPG Maker project, I'm doing something pointless but fun: there is a switch that gives all the characters Japanese names, so for every character, I have to think of a western and a Japanese name, and they have to fit together in some way. It could be a name that, by coincidence, works in both languages (like Erika, my main character); or names that sound similar (Stephanie/Satsuki); or names that are linked by meaning (Rose/Tsubaki). It might seem that I'm making things harder for myself, but I've found that having a self-imposed restriction to work with makes things much easier than starting from the usual endless list of possibilities with no clues on how to get started.