How to play saved game on different computer

You would have to transfer it across via something such as a USB storage device.

Navigate to your saves on the first computer - in Documents/Electronic Arts/The Sims 3/Saves. Copy the required save onto your USB device. Plug USB into second computer and copy save file into Documents/Electronic Arts/The Sims 3/Saves.

Then how do you access that game? I did that, but it doesn't show up when I open Sims

It should show up.

Is it still in your saves folder ? Does the folder have the extension .sims3 ?

did you place a save folder with in the save folder ? see the attached image...   if you did this then the game won't be able to read that folder so youll need to move that save folder to the desktop open it then copy your saves to the save folder in your electronicarts/thesims3/saves

or did you just open your old save folder then copy the save you want into your other save folder ?