Before you can copy anything you will need to make a selection. You can make a selection by using one of the selection tools.
Once you have made a selection you can go to the 'Edit' menu and chose 'Copy'. This will make a copy of what is in your selection on only the layer you have selected (Check the layers pallete, which one is highlighted blue?)
Go to the file you wish to paste your image into, go to the 'Edit' menu again, and click 'Paste'.
A new layer will be created with what you have copied from the other document or layer.
If this does not work be sure that you have the right layer selected and repeat the copy and paste process.
*You can make selections with many different tools
rectangular marque tools
*You can add or subtract to selections by holding down the Shift (add) of the Option (subtract) after making your initial selection
*You can use a combination of selection tools in the one selection by using the above Shift and Options keys
*You can make a selection based on one layer and then chose a different layer to copy from
*Selections can also be made by using the pen tool and creating a 'path' or using the 'quick mask' editing mode
*You can select everything in a layer by going to the 'Selection' menu and clicking 'Select all' or by using the shortcut Apple/Control 'A'
*You can cut, copy and paste by using the shortcut keys
Cut= Apple/Control 'X'
Copy= Apple/Control 'C'
Paste= Apple/Control 'V'
*When you paste, it automatically creates anew layer above the one you have selected