We just purchased a second hand dryer. It's rather old and was wired directly.. i.e. there is no plug. The cord has four wires; white, red, black and bare (ground?). What type of plug do we need?

Depends on what type of receptical,you have for the plug to fit into. Is there a receptacle ? Look at the position of the prongs for the plug.

The receptacle says 30A 125/250 V. Its Leviton.. looks just like this one
Amazon.com: Leviton 071-00278-000 4 Wire 30 Amp 250 Volt Flush Mount Dryer Receptacle: Your Store

OK now all you have to do is find the plug,that fits that receptacle.

So you need a plug NEMA #14-15P, one made by Leviton #275-T found here in their catalog:
http://assets.twacomm.com/assets/pdf/20662.pdf

Ok.. the one we bought is the second one on the page... cat number 931. How does the wiring work? The instructions aren't clear. We thought we had the wrong one.

Sorry... re read that. We do have the wrong one. Thank you!