What's the best way to crop a object out of a image without losing no detail to it?

Like so:

Before crop:


After crop:

The most painstaking method I can think of would probably be to use the magnetic lasso tool, and then erase anything leftover manually (Wouldn't suggest it for this kind of thing though).

Yea, the thing I am trying to do is crop out cars out of images for people but can't figure out how to do it good