Sounds like it's too late, you're beyond saving....
Mac apps are shipped in various methods:
- Application in a zip: your browser will either just download the zip, or extract the app as well. It's a good idea to move this to your app folder (though not essential), and then add it to your dock if you like.
- Application on a disk image (.dmg) : A nicer, Mac-ish way of distributing apps. You download the dmg file, then the OS will open the file and mount a "virtual" disk containing the app and any support files. Very often the background image on the virtual disk will include logos and instructions on how to install the app. It's very common for them to include an alias to the Applications folder, so you just drag the app onto that icon, and boom! Your app is installed. You could also double-click the app on the virtual disk, but don't do that!

If you un-mount that disk, the app is gone again! As above, add the app to your dock if you like.
- A 3rd party installer: Seems rarer these days. You run the installer they give you, for better or worse!
- A package (.pkg) file: A package, which OSX's built-in installer will open and install. These are probably most common with more complex apps, which may require frameworks to be installed, or scripts to be executed before or after installation, or helper apps to be launched. For most such packages, you'll be prompted for a username & password with administrator rights. Once installed, the apps will be in the right place, you just have to add the app to your dock if you so choose.