When using the Paintbrush tool or pencil tool in Illustrator, the lines I draw aren't copying the image i've traced over. The paths look correct while i'm doing it initially, but as soon as I release the mouse it makes it's own organic shape from the shapes i've drawn. How do I stop this from happening?
You can change the Paintbrush tool or Pencil tool options (the options for both tools are the same) to achieve a more accurate path.
The options you want to change are Fidelity and Smoothness.
From Adobe Illustrator Help:
Double-click the Pencil tool to set any of the following options:
Fidelity Controls how far you have to move your mouse or stylus before a new anchor point is added to the path. The higher the value, the smoother and less complex the path. The lower the value, the more the curves will match the pointer’s movement, resulting in sharper angles. Fidelity can range from 0.5 to 20 pixels.
Smoothness Controls the amount of smoothing applied when you use the tool. Smoothness can range from 0% to 100%. The higher the value, the smoother the path. The lower the value, the more anchor points are created, and the more the line’s irregularities are preserved.