Most of the time this is done automatically. It will ask you before playing (it will bring up a window within the screen) if you would allow ArmorGames to store data on your computer. If you select Yes, the game will allow you to save. Depending on the flash game, it will be automatically or manually.
If this does not appear when entering a flash game, then you have to do the following:
1) Tools (at the toolbar at the top) 2) Under Tools, Options 3) Go to the "Advanced" Tab 4) Under "Advanced", click the sub tab "Network" 5) Where it states "Limit Cache to _____ MB of space", enter an amount that is moderately higher than what you have. You may have too much Cache space already and ArmorGames will ask for more.