To download the clip art and animated GIFs on this site, just move your mouse over an image or animation and right-click. Then select "Save Picture As..." (or "Save Image As" if you're using a Mac). Feel free to open the pictures in your favorite graphics software, such as Photoshop, Fireworks, Gimp, etc... and edit if you wish. Keep in mind that linking to these images is not permitted.
I used clipart a LOT for newsetters and other documents. I don't always want a photo - clipart is often better at getting an idea across quickly, and I didn't need to worry about copyright because I assumed it was OK to use without permission as it was a part of the MS package. The BING option is terrible - very juvenile and hardly extensive with fewer than 50 options. And by-the-way, most of the online sites for "accessing clipart in MS Word 2010" still say to go to insert then click on clipart. Really - we hardly need such basic instructions when they aren't even correct anymore!
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!