For any icon on the Dock, just drag it away from the Dock and hold it there for a second or two before letting go. It will remove it from the Dock. Of course, this won't work on an app that's currently running. Quit the app, then do the above.
From the dock you simply drag it out. Though first you have to make sure the application is shut down and not running, then drag the application icon up from the dock (sometimes you need to drag it quite far up or around the screen I've found). You'll then notice the little trash/poof icon below your cursor while you are holding the application, let go and the icon will disappear off the dock.
For any icon on the Dock, just drag it away from the Dock and hold it there for a second or two before letting go. It will remove it from the Dock. Of course, this won't work on an app that's currently running. Quit the app, then do the above.