If your applications keep disappearing, it’s because you have not installed them properly.
When you download an program, it usually downloads as a disk image (dmg) file. (it may be a zip or compressed file that expands into a dmg). So this is what you have on your desktop when you download.
When you open the DMG file, it opens a window just like if it was a CD that you put into your machine. The installer package is in that window. Follow the instructions for installation – you either run the installer, or more commonly, you drag the package into the Application folder on your hard drive.
Once it is installed in the Application folder, then you can delete the dmg file and any other downloaded stuff from your desktop.
Then to launch the program, open the Application folder and double click on the icon of the program.
When a program opens, an icon appears in the Dock (at the bottom or the side of your desktop). When you quit the program, the icon disappears from the Dock. If you want the program to stay in your Dock, then drag the icon from your Application folder and drop it onto the Dock – this does not move the program, it just makes a permanent alias on the dock which you can use to open the program.
http://guides.macrumors.com/Installing_Applications_in_Mac_OS_X
http://www.ehow.com/how_4523131_install-programs-mac-os-x.html