You will need Java 8 to play Minecraft. If you don't have it, go get it.

If the files show up as a compressed archive (Zip/Rar) to you, or you cannot open the file by double clicking on it, first ensure you have Java installed. If you have Java installed then try using Jarfix to fix the file association.

Mineshafter Launcher

Login with whatever username or password you want. Servers should ask you to login again once you connect. Please note that you cannot connect to official servers using this. Only open servers, or those using authentication plugins will work.

Note: If you see the message "Error: Could not find or load main class info.mineshafter.GameStarter" follow these steps.
  1. Open your .minecraft directory
  2. Copy the saves directory to your Desktop
  3. Delete the .minecraft directory
  4. Start the launcher
  5. Once the .minecraft directory has re-appeared, place your backed up saves directory back inside it.