I’ve labored for hours now but I finally figured it out. If you want to use an image in Adobe Illustrator, and you want it to have round corners, here’s what you do:
1. Place your image on the artboard (File, Place)
Draw a rounded rectangle over it in the same layer
Target both the rectangle and the image(Shift + Click)
Select Clipping Mask, Make from the Object menu
So far I’m not really sure how to add a drop shadow or a border to it without creating new layers.