Macbook question

So this might seem like a dumb question to many of you. I just got myself a macbook pro, and began installing my favorite programs onto it. But every time I install a program it sets up a drive as a folder with the program and its files in it on the desktop. I can't drag it... it just gives me shortcuts, and when I eject it, the program just uninstalls. Is there any way to install the program and its files somewhere not in the desktop? I have been using a PC until now so I'm trying to figure out how to install the programs in a similar way to installing it into the C:// drive and having a shortcut in the desktop instead of the whole thing clogging up my desktop.

Any ideas?