Once you open the DMG file, on most, you will see the application icon as well as a folder right next to it called Application. If that isn't the case here, then open up Finder (the smiley face icon and the first one in your Dock) and on the left you will see the Applications folder. Now grab the icon from the window opened by the DMG and just drag it to the Application folder in Finder.
You've now installed the application..
To uninstall, you just drag the icon from the Applications folder to the Trashbin in the Dock.
The App Store is an application where you can find/buy apps for the Mac. Technically, TextWrangler is
there as well, and installing it that way will put it in the right place for you..