I used to name my characters the first thing that popped into my head. They were usually generic names or people I knew.
Then I started to check popular first names from roughly the same age as my characters (or maybe a little younger, to factor in time to get the story published). This allows me to pick a name that's right for the character and also one that might be the name of the child reading my book.
You can check out popularity of names in the US here: http://www.ssa.gov/OACT/babynames/
After I have a first name, I make up a last name. Sometimes I'll look up the last name here: http://names.mongabay.com/most_common_s
Lately I've added a new naming twist. I look up the full name on google - to see what comes up. If the name is famous or associated with adult themed things, I pick a different last name and start over.
And sometimes I still pick names just because I like them, whether they are popular or not - some names just fit certain characters.
So, how do you name your characters?