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.
There has been talk about removing Microsoft Office completely, since OpenOffice and Google has free "equivalent" products. My school district has already removed Microsoft Office from classroom student computers. Only teacher computers and computer lab computers have Microsoft installed. The future of Microsoft Office looks bleak! Their motto must be, "One step forward, two steps back!"
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!
I'm seriously angry that Clipart is gone. Why? Because many of those cheesy images were available as Vector Graphics. So, I could quickly insert a crappy clipart into my powerpoints, ungroup the elements of it and delete all but what I wanted. I used it and it worked awesome for me multiple times. I wrote clipart off for years and only started doing this in the past 2 years...I wish I had known earlier.
I use clipart often and transport it into other programs such as Print Master to make cards. It was easy to make a few small changes in it and use what you redesigned. I hope you'll reconsider it's removal and put it back. Personally, I don't care for Bing's images. And I don't want to go out on the net to find other clipart when I'm in the process of getting a manuscript together. It's a waste of time.