You need to double-click the icon on the desktop. Then, in the window that comes up, you do one of two things:
a) for Firefox, you drag the Firefox icon to the Applications folder
b) for Flash, you double click the icon to start the installer
After the programs are installed, then you can drag the icons on the desktop to the trash. (the icons on the desktop are mounted disk images that are used for installation, not the actual programs themselves)