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 applies more to teachers than to anyone else, but clip art (especially black line clip art) can´t be beat when it comes to using images that are going to be photocopied. It creates a much cleaner look than a photo. While there is much talk of going digital, the reality is that most of the world still is using paper for teaching . . . and a lot of it, not because we aren´t open to the digital world, but many times not all students have access.
I liked it for the simple inserting of visual effects for creating newsletters. Pictures do enhance communication and the ease of using a word document and gathering an image made this task easy. Now having to go outside of my document to find the extra spice my documents need makes this less fun. I have always used animated images that were less than artistic but were entertaining. Like others I will miss this service, but I understand progress is not always comfortable.
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.