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.
Is there a potential downside? Yes. Just because a search engine sees something as Creative Commons doesn’t necessarily mean that it is. Here at MakeUseOf, for example, we’ve had at least one photographer threaten to sue us over an image he didn’t realize he himself licensed as Creative Content. He backed down when we pointed this out, and it’s one example resulting from thousands of blog posts spread over a decade, but know that this isn’t without risk.
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.
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!"
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.
My school district doesn't allow students to access anything except Google; therefore, clipart is useless. More and more school districts and companies are blocking applications and websites to prevent access to inappropriate images and content. My first and second graders have always loved doing PowerPoints; however, with clipart no longer working, they cannot do these projects any longer. Older students access Google images to get graphics for their projects.