Let\'s take the whalesay images as an example. docker history shows the following:
IMAGE               CREATED             CREATED BY                    
        I don't really understand what you mean by "extract" but if you want to get further information about image, run
docker inspect <image_name>
You you want to get file, then run container from this image. Try
docker export <container_name> > abc.tar
after that, extract abc.tar and find your file.
While not capable of extracting a specific layer, the docker-save-last-layer command line utility is made to extract the last layer only. Combined with docker build --squash you can avoid exporting the base layers. This may help to accomplish your goals.
It works by using a patched version of the docker daemon inside a docker image that can access the images on your host machine. So it doesn't require doing a full docker save before using it. This makes it performant for large base images.
Typical usage is simple and looks like:
pip install d-save-last
docker build --t myimage --squash .
d-save-last myimage -o ./myimage.tar
                                                                        In this specific case, it looks like the ADD command added the base image to the file system.  If you run docker history --no-trunc docker/whalesay, the full command is:
/bin/sh -c #(nop) ADD file:f4d7b4b3402b5c53f266bb7fdd7e728493d9a17f9ef20c8cb1b4759b6e66b70f in /
docker history reports that particular layer is 188MB.  Let's look at these layers in more detail:
$ docker save docker/whalesay -o whalesay.tar
$ tar tvf whalesay.tar
...
-rw-r--r-- 0/0       197181952 2015-05-25 22:04 cc88f763e297503d2407d6b462b2b390a6fd006b30f51c8efa03dd88fa801b89/layer.tar
...
Looks like a pretty good candidate! You can now extract that layer and pull files out of it.
$ tar xf whalesay.tar cc88f763e297503d2407d6b462b2b390a6fd006b30f51c8efa03dd88fa801b89/layer.tar
$ tar xf cc88f763e297503d2407d6b462b2b390a6fd006b30f51c8efa03dd88fa801b89/layer.tar etc/passwd
If you're looking to pull a particular file out of a layer, but you don't know which layer, you could do this. First, extract all the layers:
$ tar xf whalesay.tar
Now you've got all the layers as individual .tar files. Let's find a file:
$ for layer in */layer.tar; do tar -tf $layer | grep docker.cow && echo $layer; done
usr/local/share/cows/docker.cow
0523c5a0c4588dde33d61d171c41c2dc5c829db359f4d56ab896ab1c185ed936/layer.tar
cowsay/cows/docker.cow
40e8ae7bb4e5b9eaac56f5be7aa614ed50f163020c87ba59e905e01ef0af0a4f/layer.tar
cowsay/cows/docker.cow
f9bc8676543761ff3033813257937aeb77e9bc84296eaf025e27fe01643927cf/layer.tar
Finally, extract the file from the layer you want:
$ tar xf 0523c5a0c4588dde33d61d171c41c2dc5c829db359f4d56ab896ab1c185ed936/layer.tar \
      usr/local/share/cows/docker.cow
This will extract that file with the full path relative to the current directory.
$ cat usr/local/share/cows/docker.cow 
##
## Docker Cow
##
$the_cow = <<EOC;
    $thoughts
     $thoughts
      $thoughts     
                    ##        .            
              ## ## ##       ==            
           ## ## ## ##      ===            
       /""""""""""""""""\___/ ===        
  ~~~ {~~ ~~~~ ~~~ ~~~~ ~~ ~ /  ===- ~~~   
       \\______ o          __/            
        \\    \\        __/             
          \\____\\______/   
EOC
                                                                        Docker is not capable of saving layers individually, however there is a tool on Github called dlgrab that claims to do it. https://github.com/aidanhs/dlgrab
It looks like other people would also like to have this feature, but unfortunately right now it does not seem to exist.
See also this issue and here a related request which got rejected.
If you're fine with saving the complete docker (docker save) and then extracting a tarball with your layer, then this is possible:
docker run -it <your image>
# do fancy stuff in the container
docker commit <your container> foobar # create image from container
docker history foobar # will show you the layers
docker save -o foobar.tar foobar # dumps container contents to foobar.tar
Now foobar.tar will contain the file system states from different times.  Inspecting this tarball shows, in my case, a file repositories with
{"foobar":{"latest":"fdf43d96e691c57e9afb4b85dba2e6745146a7ca9076c7284c6b2e1f93434562"}}
which indicates, that the latest layer is fdf43....  You can get a tarball with the file system contents of this layer via
tar -x fdf43d96e691c57e9afb4b85dba2e6745146a7ca9076c7284c6b2e1f93434562/layer.tar -f foobar.tar
There is a tool, undocker, which automated this process, but I'm not sure whether it will work with the current format of the saved tar file.