How can I control time?

It is a special "Notch power" not available to players — it was used by the Minecraft developers for debugging. It was accidentally released in the first pre-release of Beta 1.8, but was taken out for the second one and the "stable beta" release.

The only way of controlling time is the operator-only /time command on multiplayer servers, which is instantaneous (unlike the effect shown in the video).

You will be able to control the time of day in creative mode.

1.8 will add Creative Mode

Since the Adventure mode will be replacing Survival, Mojang has also re-implemented Creative mode! In this mode, players will take no damage, be able to fly, control day/night directly, can spawn infinite items of any type, and can break blocks with one hit!

It's enabled by default in MineCraft 1.8-pre_release single-player. In both Creative Game Mode and in Survival Game Mode. Press F6 to forward time and F7 to rewind time.

As of Minecraft 1.8, you can no longer control time with F6 or F7, neither in Creative mode nor in Survival mode.