How do I make a shortcut to an origin game?
Assuming windows 7, you should already have a shortcut available in your windows Games folder. For me, this is located at C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Games.
Alternatively, if you hit the start button (or windows key) and type "games explorer" and open the folder it displays, it will list all your registered games. 
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From either of these folders, you should be able to right-click-drag the game's icon onto the desktop, and selecting either copy here (games folder) or create shortcuts here (games explorer)
Dave's answer can show you one way to create a shortcut, but if you don't see the game you're looking for listed there, you have another option. For most games, the steps below will let you find the target .exe that you can manually create a shortcut to.
In Origin, you click on the Gear icon and choose Settings.
Look at the directory listed for "Downloaded Games".
Navigate to that directory in Windows. The game you're looking for should have a folder with its name here.
Usually for a game, there's an .exe with the game's name either in the base folder for that game, or under a /bin folder. You have to dig a little deeper for Mass Effect 3 than most. For Mass Effect 3 in particular, the .exe you want is under ~/Mass Effect 3/Binaries/Win32/MassEffect3.exe. Every game is going to be a little bit different, but it's usually not too hard to identify which .exe will launch the game.
Having identified the .exe, right-click on it and select Send To->Desktop (create shortcut) from the context menu.
