You can make your own finger paints by mixing 2 tablespoons of white flour with a little water to make a thin paste and then adding a few drops of food coloring.
To make painting extra easy for a young child, have her paint on waxed paper taped to a table in the kitchen or outdoors. Put a blob of paint down on the paper and show her how to slide her fingers around. If you want to save her creation, press a piece of regular paper over the waxed paper and peel gently away; hang to dry.
I personally used normal paper and it worked fine. This does not make the best paints in the world but it really amuses a baby. Best of all you know it's non-toxic. She kept eating it and it was great to have the piece of mind of knowing it was just coloured flour and water.