This is a very individual process, but I think a few words on the subject might be helpful.
Dickens is the master of meaningful names. Names like M'Choakumchild instantly signify who the character is in the readers mind. Your names don't have to be Dickensian, but they should mean something. And just keep in mind that there are inherent differences between names like Kenneth Elsington III and Butch.
What I usually do is have a picture of my character in my head. I try and grasp them as a person, both their personality and how they look. Then I try and find a name that matches, even if there's no real logic behind it. I sometimes like to have a significant meaning behind the names I choose, too.
Here are my favorite baby name sites to help you pick names: