What is the easiest way to find a family member online [for free]?

Well, yesterday I have just discovered my dad has a half-sister. My grandfather [my dad’s dad] abandoned him as a child and his real mother [my real grandmother] re-married [i already know]; but I did not know he had a half-sister. I found a few pictures in an envelope she has sent my father looong ago and I would really like to try and get in touch with her!
What is the easiest way to find her online for free [apparently you CAN put a price on family in certain websites]? I try finding her on facebook; i type in her name and there are like four results [none of them with a default pic]. If it helps, here is what I know about her so far: African-American, female, [last whereabouts; Los Angeles], name: Diane McKinney [McKinney is her married name; Diane Wren is her maiden name]. I really need help and can use all I can get! Please and thank you all :)