What can I do to ensure I only erase the smaller details without affecting the area around it? I don't draw much and can't even call myself an amateur yet. As a result I make a lot of mistakes and also many test strokes when drawing. 

For small touch ups and mistakes the eraser is my best friend. However, my big white eraser does not help much when I need to only make small corrections. It can remove larger areas around where I am erasing. 

Let's say I am talking about erasing small areas less than a centimeter in diameter. What can I do to make my erasing more targeted and only affect the areas I want to remove?
Get an erasing shield/stencil:



An erasing shield is a metal stencil that can mask off the parts of your drawing you want to protect, while exposing only the area you want to erase, so you can erase with more precision.