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.
While most references to Clip Art disappeared with Office 2013, users were able to insert the old-school images into documents using an Office.com Clip Art option. That is now being replaced by Bing Images, with Microsoft filtering images to ensure they’re based on the Creative Commons licensing system for personal or commercial use. Most of the new images are much more modern, instead of the illustrated remnants of the past. Clip Art might be facing the same Office-related demise as the great Clippy assistant, but let the images below remind you of the good old times before the modern-era takeover.
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!
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.