I am 21 and I have a 7am to 3 pm job and I attend college full time over the internet my childes mother is 19 and dropped out of high school because she believed that she needed to in order to take care of my child. She says that she was going to return to school but instead she has started to do drugs and parties all of the time. She has a part time job no insurance and she still lives at home with her mother. I have a full time job full benefits a car and I am drug free what ways could I prove to the judge that she she is an unfit mother with jeapordizing hurting her or my child with all of the non sense.

I do not know the legal aspect of it... but I would imagine you should keep a detailed record of situations in which you have seen her on drugs... If she is really doing this you need to take immediate action and get your kid out of that situation... You have to stay focused and remember that it will not be easy... but your love for your child should conquer it all... I would get some legal help as soon as possible... remember that if she is on drugs she is not making sound decisions... you need to first think about your child.. and then maybe later you can try to get her help... for your child's sake

From what I have seen children's services do not typically take kids off drug addicted parents unless there are extenuating circumstances that could pose a threat to the kids.
I even know drug addicts that their lifestyle is very detrimental to the kids and they still do not lose them.
Since she is living with her parents they tend to look at it as a more family friendly environment also.
All you can do is document everything possible like phreekid said that you see as a problem and go to family court to work out custody and visitation. It will then be up to the Judge to make a decision on everything.