If you need a high quality image file and all you have is a Microsoft Word document, I feel your pain. The high quality image may have been placed into the Word document, but getting the image back out without losing quality is another matter.
So far, I have not found any suitable tools for doing just this task. (Update: I discovered a tool and added it as Method 3.) I would be very happy to learn of them. In the following, I present two methods that work to achieve this goal but neither method is perfect. Both of these methods were developed and tested using Microsoft Word X for Macintosh.
Because of the different versions of Microsoft Word and the variations between installations, I won't present detailed instructions here. I will present the techniques and let you figure out how to implement them in your version of Microsoft Word.
Very often, high quality images are scaled by the document's author to fit on the page. To resize the image, select the image and change the Picture Format. To make the image into the original aspect ratio, set the size to have equal percentage values for horzontal and vertical size.
Method 1: Copying and Pasting
In order to use the copy and paste method of extracting the image, you first must resize the image to be 100% size. If you can't achieve 100%, then you need to make it as large a percentage as you can get away with. The size limit is imposed by Microsoft Word's understanding of the working paper size. To increase your paper size, define a custom paper size for the document. Make it 22 inches square. That is the largest paper size permitted (at least that is the largest permitted in Microsoft Word X for Macintosh).
With the image as close to its original size as possible, copy the image and paste it into your choice of image editing software. If you were able to achieve 100% size for the image in Microsoft Word, then the pasted image should be the original quality, or lacking that, it will be the best quality that Microsoft Word will give you for that image.
This method will fail to give you the best quality if the original image is too large to fit within the maximum paper size of 22 inches. This is governed by the dots per inch specification in the original image.
Method 2: Web Page Export
Depending upon your installation of Microsoft Word, it may have the facility to save the document as a web page ("save as HTML"). When doing so, any images in the document will be converted to image files. The trick will be to force these images to be very high quality.
After you have changed the Picture Format to be a 1:1 aspect ratio, choose to save the document as a web page. In the Web Options, choose the largest monitor size available. Specify 600 dpi. That should be plenty. If you know your original image is a higher dpi, enter something higher if it permits it.
Choose to save the document. Microsoft Word will create a subfolder using the name you chose with "_files" appended to it. You will find high resolution JPEG images inside this folder. These images will be at the original document's dpi or your choice of dpi, whichever is smaller.
This method can only provide you with JPEG or GIF files (or potentially PNG images). Since both of these formats are lossy, you might not be able to get the best quality but it should be pretty good. JPEG is lossy in the image quality while GIF is lossy in the color spectrum.
Method 3: Using a Third-Party Software Tool
If you use Mac OS X, you can use a tool called File Juicer. It will automatically find any type of image, pull it out of the Microsoft Word file, and save it into a separate file. It will extract all images it finds. It is not limited to processing Microsoft Word files. The method it uses can operate on any type of document you suspect contains image data.