How to Delete Icons in Mountain Lion
To get rid of an icon — any icon — merely drag it onto the Trash icon on your Mountain Lion Dock. Trashing an alias gets rid of only the alias, not the parent file. But trashing a document, folder, or application icon puts it in the Trash, where it will be deleted permanently the next time you empty the Trash.
The Finder menu offers a couple of commands that help you manage the Trash:
Finder→Empty Trash: This command deletes all items in the Trash from your hard drive, period.
Use this command with a modicum of caution. After a file is dragged into the Trash and the Trash is emptied, the file is gone, gone, gone unless you have a Time Machine or other backup. (Okay, maybe ProSoft Engineering’s Data Rescue II or some other third-party utility can bring it back, but don’t bet the farm on it.)
Finder→Secure Empty Trash: Choosing this command makes the chance of recovery by even the most ardent hacker or expensive disk-recovery tool difficult to virtually impossible. Now the portion of the disk that held the files you’re deleting will be overwritten with randomly generated gibberish. You’re hosed unless you have a Time Machine or other backup.
If you put something in the Trash by accident, you can almost always return it whence it came: Just invoke the magical Undo command. Choose Edit→Undo or press cmd+Z. The accidentally trashed file returns to its original location. Usually.
Unfortunately, Undo doesn’t work every time — and it remembers only the very last action that you performed when it does work — so don’t rely on it too much.