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Switching Mac Missing Manual. Snow Leopard edition. This will cover the basics of the similarities and fiferences between Windows and Mac OS X so you can better understand how to move between them.
The Dock is merely a shortcut point for applications, documents, minimized windows (with the yellow minimize button), and folders (sometimes stacks if viewed that way), and the trash to reside. Unlike the Windows toolbar, it is not a folder onto itself, and the only way to get info on an item is to click it, and wait for a menu to pull off of it. Applications on the dock only stay there as long as they are open, or if you use the menu from clicking once on it to keep it on the dock. It may not be at first obvious, but below the application is a dot or triangle to indicate it is open, when it is open.
Close all open windows with the red buttons and see if the application ended up on the desktop (in the wallpaper area) to see if you misfired when moving the application initially, and move it back to where you first found it, if you did.
A very common mistake some people do, is drag the application from a disk image to the Dock, then close the disk image, or reboot and the disk image is unmounted. The Disk Image is an icon that many installers and applications start out from which is a virtual disk that shows on your machine when you open a .dmg or .img file. If there is no installer, and all you see is a folder or application inside that file, drag it to your hard drive's application folder. Then depending on your Dock's orientation either drag it to the top of the dock on the left or right, or the left side of the dock if the dock is on the bottom of the screen.
Do not drag the disk image icon to the trash, because that will dismount the disk image and treat it as if you ejected a real disk that contains the installer. If there is a disk image file there (.dmg or .img), move it back to the desktop, so you can reopen it and move the application to the correct folder.