Scratch

You can't copy and paste...but you can drag and drop.  First, you need to get the picture you want into a file on your computer.  If the picture you want is on the web somewhere, try right-clicking (alt-click for Mac) and looking for a Save Picture option or something similar.  I always save to my desktop so it is easy to find them.  Then, open up Scratch and position it so you can see the part of the desktop where the picture file is saved.  Click on the sprite you want to add the picture to as a costume. Then, just drag the picture over and drop it in the costume area.