How to update game for happenings while player is away?

I want to make a game that allows the player to gain resources/progress while away from the game.

Examples: Tiny Tower, Pixel People, Some components of Plants vs Zombies.

There is no multiplayer component intended. I just want the game to calculate the resources/events that occurred while the player was away from the game.

As a related question, I'd love to have the save files on the cloud (like steam cloud or a cheap service/server). Can anyone point me in a direction for learning more?

Thanks!