What is it you are trying to install using a disc? Is it Mac Software or 3rd Party Software?
When you download something using Mac OS, the file usually arrives on your desktop in what's called a 'Container', be it a .zip, .dmg, .sit, etc.
All that's needed is to double-click the 'Container File' and in doing this you are launching the contained Volume which looks like an external Hard Drive icon.
Usually this mounted Volume then auto-opens with the contents finally revealed. It's usually required that you drag the app from this mounted Volume to your Apps folder. If you are not Admin then you will be prompted for the Username/Password.
Once installed in your Apps folder, go there to launch the App and the Apps icon will appear in your Dock and bounce to indicate it's launching. If you right/control-click the Dock icon you can select to keep it there after you quit it.
Finally, you need to eject the mounted Volume by dragging it to the Trash, which in turn will transform into the eject icon. Drag the volume over this eject icon to finish.