Moving a file with TortoiseHG is simple, if not quite intuitive.  Unfortunately there is no “Move” command, instead you need to use the rename dialog.

First , left click the file you want to move, and select “Rename File…” from the TortoiseHG context menu.  You will see the following dialog:

To move the file, delete the “Destination” text box, then press “Browse” to bring up the file browser.  From there, select the directory you want to move the file to:

You can also just type the directory directly in the destination box.  Press “Rename” and you are done.

If you want to copy a file, follow the same procedure but select the “Copy source -> destination” check box.