What should I do to stop my daughter from sucking her finger...

How old is your daughter? This is a relaxation for some children and a matter of security for others. If she is going through some changes it may be best to wait a while.

My daughter was 5 and all I did was tell her that she was a big girl now and big girls did not suck their fingers. She asked each night if she could suck her fingers but I said no. That lasted about a week and she never did it again.

My 4 1/2 year old is another matter. He is a little more stubborn, but he is in a transition period from daycare to "big boy" elementary school, so I am not being as tough as I could while he gets used to the new routine and the new people.

If your daughter is very young, then I wouldn't worry about it. If she is an older child and is still sucking on her thumb by her first adult tooth, then I would put gloves on her hand to remind her not to suck her thumb.

Or try a pacifier

Well my daughter is 13 and she still sucks her thumb due to her having her dummy taken off her at a young age
She usually sucks her thumb when she is tierd or bored
It has effected her front tooth quite bad

Do nothing. The great majority of thumb suckers don't damage their health and it's a great habit to have for relaxation, concentration, sleep, etc.