As always there are several different methods of duplicating a layer in Photoshop. You will normally have a preferred way of working in photoshop, so choose whichever way fits in with your current processes the best. There is no right and wrong way, there are in fact 6 ways!
Please note: All the methods describe below involve having the layer that you want to duplicate selected in the layers palette as an initial step.
Right click the layer in the layers palette and choose duplicate layer from the drop down list that appears.
Click the layer options (top right on the layers palette) and choose duplicate layer.
Drag the layer onto the new layer icon at the bottom of the layers palette.
Go to the top menu and choose Layer > Duplicate layer
With the marquee, lasso or crop tool selected right click the canvas and choose duplicate layer.
Press Ctrl + J / Apple + J