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 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.
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.
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.
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.
The download marketplace offers a variety of products and resources that you can download to create better documents and presentations. This download section contains add-ons for Microsoft Office like this Attachmetric that helps to tracks who has opened your emails and attachments or ClearContext Professional to prioritize, organize, color-code, manage Outlook in a better way.