How can I get my six year old to stop sucking on her finger?

She'll stop someday. Thumb sucking is quite common and if it is not to the point of peeling her thumb skin off, she will get tired of it some day. Keeping her busy will help. If u really don't want her to do so, put some peppermint or tobasco sauce on his thumbs, she won't like it and will give up after awhile. A little bit of tobasco sauce may seem a bit mean, but i never seen a kid hurt by it. Good luck.
See an orthodontist! Thumb sucking is a difficult habit to break at age 6 and without any professional help. Your child's dentist, pediatric dentist or an orthodontist can help stop his/her thumb sucking with the use of a habit prohibiting appliance. An orthodontist can also evaluate and address any malocclusion (incorrect bite) that may have been caused from thumb sucking.
See an orthodontist. We have appliances that can help stop this habit without causing your daughter pain.
Thumb sucking. Try behavioral modification therapy. Take baby steps. If your child sucks the thumb while watching tv then initially have her sit on her hands while a commercial is on. Then later switch to no thumb during the show.
Need a coach. You cannot make her, she will need to decide to stop. Finding a good coach is key. That may be your pediatric dentist or orthodontic specialist. After the age of 7, our powers to rationalize cause and effect come into play. She may then begin to understand the damage that her finger sucking may cause to her teeth and make the decision to stop with some outside coaching.
Worth her while. Kids will only break a habit if you can make them want to stop it. It's a comfort issue for her, and she won't stop until she really wants to. One program that helps is "unplugging the thumb". Sometimes an incentive program (if you go the morning or the afternoon without sucking, you get a star. 5 stars and you get a small prize, etc) may focus the child. Friends and school will point it out too.