I was adopted when I was three months old. I found out that I was adopted about five months ago after asking my parents about the odd circumstances surrounding my birth. My mother told me my biological mothers name but that was no help in finding her as she was unlisted. Eventually my crazy biological dad contacted me and I got in contact with my bio-mothers sister through him.
Your situation is reverse of mine though. Your seeking her, and don't have a starting point.
It'd help if your mother could tell you who the child was adopted out to, she had to sign papers to do so and so should more than likely know who. It will help greatly if you can find out who the male is that adopted her as of womens last names change with marriage & divorce. If you can get a hold of that person then you can likely find your sister or information on her to find her. It is a very touchy subject with parents as my mom had a breakdown when I finally got her to tell me. They are afraid of rejection or disappointment. It could also affect your sister hard from finding this information out if she does not already know. To the point of disbelief.
The name of your sister could changed like mine did as well. Mine went from Tina Meadows to Heather Hopper making it hard for family who was looking for me to find me.
But again try to talk to your mother, be patient, go slow. And tell her how much it means to you to find your sister. And if she co-operates she will at least give you the first clue to finding her.
In the money department you can always hire someone to find her for you, they have agency's that focus on lost adoptions. But they can get rather pricey.
Good Luck!