I've got my printer scanner, copper properly installed, but I can't seem to figure out how to scan a document. I'm on a Mac mini and use OS X 10.9.4. Before my laptop died, I had an icon in the dock that I could simply right click on and there you'd go.
There are several methods of scanning from HP all in ones.
Using System Preferences > Printers & Scanners, selecting Scan and the Open Scanner button which will open a Scanner Window.
In the Printers & Scanners preference pane there's a Printers List on the left hand side where you can drag the icon of a scanner equipped printer to the desktop. When clicking that Desktop icon (a short cut) a window will pop up for that printer with a Scanner button that will open the same Scanner Window.
Some HP printers at least historically came with HP applications which included a Scanner App (e.g. HP Scan.app) where you could have created a short cut to an HP Scan.app and placed it on the Desktop. If your Applications or other installation Folder had been dragged to your Dock, that could have been done as simply as dragging the icon to the Desktop. (I have a set of HP Applications that came with my old HP 5610 that includes OCR, so I keep that around. You may find you have better control over resolution a well.)
If you have an application open, you can keep it available in the Dock by right clicking it > Options and selecting Keep In Dock. You can then launch it from the Dock as well as select it if it is running.
While in the Finder, you can select Help in the Toolbar, enter the search term
scanner and you'll see various Help Topics on performing scanning.