Hi Graham412,
you're playing "On-line" chess which is analolgous to playing chess by mail. You are allowed one legal move, and then you have to wait for your opponent to respond. to move, place the cursor over one of the white pieces (you're playing white in the game you started), click and hold the button down, while holding the button down drag the mouse to the square you want the piece to go to. It has to be a legal move or it won't work.
If you want to try this in a more immediate environment, go to "Live Chess" where you will be able to play with moves happening within seconds instead of days. It might give you confidence that at least you're mechanically using the interface correctly.
I just joined this site January 28, 2011 and trying to play my first game. I can't move the pieces. They don't seem to drag and drop. They don't click and move. How do you get these pieces to move? Thanks in advance.