If you mean your own artwork, then you'd take a picture of it, upload it to your computer (make sure you know where you're saving it), then select Insert > Picture in Word, browse in the location where you saved the photo, click the picture, and insert. If you mean an image from the internet or something, you can just save it to your computer and basically follow the rest of the steps above.
This pretty seriously ticks me off. Why in the world would a company delete something that far ranging without at least sending an email to the customer or broadcasting it on every platform possible? I used clip art on a regular basis....making cards, mailing labels, chore charts, papers for my homeschool, etc. It would have been nice to be able to save off all those clip art graphics to my own drive before MS Office did one of their lovely updates and removed everything. Personally, I detest Bing and I'm not even remotely interested in getting involved with anything involving copyright law. Maybe it's time to make the journey to Open Office at last. Buh bye Microsoft!
Bing Image Search uses a copyright filter based on the Creative Commons licensing system. The results that are returned are images that have been tagged with Creative Commons licenses. A link to the source of the image is provided, which you should use to review the source of the image and the applicable license to determine whether your use will comply with the license. (The settings can be switched to show all web results to view more images.) However, you are responsible for respecting others’ rights, including copyright. Learn more here.
This is TERRIBLE! Besides being able to edit vector images like Will mentioned (which is important for those of us who don't have graphic artists available to create custom images or the budget or time to buy that service ad hoc), you could also search for style "families" (different graphics that were all in the same style). There was a huge range of files and styles in the collection and it was much faster to find what you need than to do a Bing search. Plus, you knew that everything there was free and free to use, without having to worry about CC license issues.