You need to create an account to get access to ‘My Games’ from any computer. When you don’t have an account you can only save games to your own computer. But when you remove the cookies on your computer, all added games will be removed also.
You can easily add a game to ‘My Games’ by clicking on the picture of the diskette, on the game page in the upper right corner of a game or under a game on the tab ‘Game Information’.
You can remove a game from ‘My Games’ by clicking on the cross at the upper right corner of the game you want to remove, on the ‘My Games’ page.