Looking for someone!?

So basically whats happened is that my mother left me when i was just a baby. Recently at the age of 27 I have been wanting to find her to get some answers. My dad told me she left because she couldnt take care of me responsibly, but my grandmother told me he used to beat her and had a gambling problem. But i've never seen him touch cards but he does have a bad temper. I know her name and her younger brother's name and they both moved from Korea to Hawaii to California thats all the info i got. Guess My question is what steps should I take to go find her? I dont want to hire a private I though, I'd like to keep this a secret for my own reasons. Thx in advance