The .dmg will mount on the desktop. When you open the .dmg, there will be a window with the app inside that you can: a)click on to open the app or b) drag that icon to your applications folder in Finder to install. (Some of them will have the app and an icon of the Applications folder in the window that the dmg opens, in which case, just drag and drop the app icon onto the Applications folder right there within the window to install it.)
Once you have installed the app, then you can close the window, eject the .dmg and delete it.
The type of apps that are just drag and drop to install, all you have to do to uninstall them, is right click on it and select delete.
Some apps have an actual installation routine like you are familiar with in windows. Those type of apps will typically also have an uninstallation routine to delete them.