Installing apps from the downloads folder

I've downloaded Filezilla (since it's something that I'm familiar with from my PC) After clicking it a few times in the downloads folder, I was able to open it and set up the settings for my website. (It doesn't make a connection yet but that's another problem.)
The issue I'm having is that when I closed Filezilla after setting up my first site. It disappeared. I could not locate it again in Applications or the Launchpad. I can access it again from the downloads folder and it did retain my settings but I'm assuming that downloads are not meant to continue to accumulate in the downloads folder.

Hoping you patient people can tell me what I'm missing.
Thanks

Have a read through here and see if it will point out the step you're missing.

http://www.mac-forums.com/forums/switcher-hangout/251468-installing-uninstalling-applications.html

You're probably just missing dragging it to the application folder after you open the dmg file - but have a read through - that should explain it better for you.

bobtomay said:

...after you open the dmg file -

Click to expand...

??? Did you mean after you download the dmg file? Or am I mis-remembering something? I don't do this often! (download an app, that is)

No, after you download a dmg, you need to open the dmg file prior to being able to install it.
You don't just drag the dmg file to your applications folder.