If you're running on Windows and just want to set up a server easily, download Minecraft_Server.exe and run it.
If you want to run the server on any other OS or without GUI it's a bit more involved. First make sure you can use java from the command line. On Linux and Mac OS X this should already be set up but on Windows you might have to tinker with the PATH environment variable. Download and run minecraft_server.jar (621 KB) with java -Xmx1024M -Xms1024M -jar minecraft_server.jar nogui.

Below are some video's installing a Minecraft Server:

Microsoft

Mac OS X

Linux

Buy and download

You first need to buy the game before you can download it on the Minecraft website. It will automatically update the game files to the latest version. It's possible to play offline if you run the game online once.

Microsoft Windows

Download Minecraft.exe, place it anywhere you want, then run it.

Mac OS X

Download Minecraft.zip. Unpack and place Minecraft in your /Applications folder.

Minecraft for Linux / Other

Download Minecraft.jar, an executable jar file. It might work as-is.
If you run into out of memory errors, try launching it with java -Xmx1024M -Xms512M -cp Minecraft.jar net.minecraft.LauncherFrame
Also, please make sure you’re running the Sun JVM…

Minecraft Server

You can check this youtube movie if you want to setup your own Minecraft Multiplayer Server

I always buy my t-shirts an other fan stuff at http://www.jinx.com/shop/coll/minecraft/.

They have a lot of Minecraft t-shirts so it's worth to have a look.
Have fun!