In SharePoint 2007 and 2010 we moved web parts by dragging them. That's still true for SharePoint 2013 web part pages, but for the wiki-style home pages you now cut and paste them! That's an improvement for consistency in home page editing, but also means that users need to know two ways to work with web parts.
Now for the details:
- You can't Right-Click and Copy or Cut (no option in the popup menu)
- You can't click the Copy or Cut buttons in the ribbon (unless you also include some non-web part text in your copy selection)
- You can use Ctrl-C or Ctrl-X followed by a Ctrl-V in the new location if you first click the title bar area of the web part. The results are the same for both Copy and Cut. I.e. Copy followed by a Paste is actually a Cut and Paste operation. (strange!) (So, if you want two of the same web part you have to insert it twice, not copy and paste.)
- Copy of a web part from page A to page B looks like it works, but does not. The web part appears in page B when you paste, but disappears when you click Save. (Bug!)