This page contains information about hosting your own Minecraft server.

The official Minecraft Wiki has a detailed instruction page concerning how to install a Minecraft server on Windows, Linux, or Mac.  The link is included here rather than reinventing the wheel, but there are some addendums.

1. Check your school's Acceptable Use Policy (AUP).  Minecraft can be played using a web browser, but the server is additional software.  You may need permission before installing it (not to mention changing ports) on a school computer.
2. If you are unable (or unwilling) to install the server on your own computer or a school's computer, you can rent server space from a number of providers.  Servercraft.co  and minecraftserverhost.net offer dedicated Minecraft servers, but you can also install it on a Virtual Private Server, or VPS.  Dreamhost is one of the more common web hosts out there that offers this service.  Keep in mind that the less RAM you have free on your server the more performance issues you will encounter.

Related Notes:

In Pender County Schools we will be hosting a virtualized Minecraft server on our district's local network.  It looks as though we'll be running Linux/Ubuntu and will be starting with about 3GB of available RAM.  Once this is running and we begin to test it, we'll add additional technical notes.