I think there might be some confusion here. While some applications install by simply dragging them to the Applications folder, NeoOffice is not one of them - it has an installer program (.pkg file) that you double-click, which in turn runs a setup wizard. Once the wizard completes, you'll find a NeoOffice icon in your Applications folder.
If you downloaded the right program file from the NeoOffice website, you double-click on it, which mounts it as a virtual drive. Open the virtual drive (this should happen automatically when you double-click the NeoOffice file) and then double click on the NeoOffice.pkg file to run the installer.