If you're stuck on the demo mode after purchasing Minecraft, please visit this article.
If you would like to try Minecraft before deciding to make a purchase, you can play the demo mode by registering for an account, then downloading the Minecraft launcher. This version of the game lasts five in-game days, or about 100 minutes.
The demo mode is available to any Mojang account that is logged into the launcher, but does not own a copy of Minecraft.
When you select Play Demo from the launcher, you'll be taken to the game's main screen with the option to start/continue a demo game, or reset the demo and start over from the beginning.
Playing the demo mode is a useful way to see if your system can run Minecraft. For more information, please also see the system requirements.