For me, character names are just kind of a feel, and I use all kinds of methods. Even within the same books.
Like in Me, Just Different.
Skylar is a name I've loved for so long that I'm not even sure where I first heard it. Her full name is Skylar Lynn Hoyt because when I first came up with it (6th grade?) my initials were also SLH, and Skylar was my "me" character in stories. So it's a little funny to me that she ended up being my polar opposite in my debut series.
I wasn't having much luck coming up with a name for Skylar's guy. I finally found Connor's name while driving on I-70. I got stuck behind a semi that said something like Connor Trucking. As soon as I saw it, I was like, "That's it! That's the name!" (Though now that I'm about to have a son named Connor, I need to come up with a better story than that.)
Jodi was my best friend in middle school, and we actually found ourselves in a similar predicament as Skylar and book-Jodi. Especially when it became clear to me that the Jodi character was my villain, I planned to find Jodi a new name. But real-life-Jodi was totally excited about having her name in the book and asked me to keep it.
Eli is just a name I've always loved. I actually had a Jack Russell Terrier named Eli. Who's also has a "I'll do whatever I want, and just try to stop me," kind of personality, so it works out well. Oddly, I once got teased for this name. Back in 2007 at a conference, an acquisitions editor was like, "Where did you get the name Eli from? It sounds Amish or something." In 2009, a month before Me, Just Different released, Sarah Dessen released Along for the Ride. Main guy's name? Eli. Take that Acquisitions Editor!
These days, when I start a new book, I spend a lot of time on Babynames.com. I'm apparently not the only writer who does this, because they now have an article on their site with tips for writers.
So. How do you name your characters?