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There is an option on the downloaded version that says "play offline" click that.
If you have access to an account that has bought Minecraft, which is hard to do for free, then you can play in-browser and download the launcher to play offline.
You can bring a flash drive in, and put .minecraft and minecraft.jar in the school computer and thus run the .jar and play minecraft offline, on any worlds.
Enter no password, and the options will appear of 'play offline' or 'try again'. Select play offline.
In order to download Minecraft - legally - you must buy it as a registered user. It is a one time purchase of $26, and once bought you can even play offline! Once you have it bought, login to account wait for the files to download. After you finish this up, you can then exit Minecraft and login (password at this point is not needed if you wish to play offline) and reopen Minecraft and login. You have the option of playing offline. Click it, and you are now playing offline!