If you have bought the game, you can download a stand-alone launcher for Minecraft here.
It will automatically update the game files with the latest version.
You will be able to play the game without an internet connection if you’ve run the launcher at least once while connected to the internet.
Download Minecraft.zip, extract the Minecraft app, then run it.
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…
Multiplayer beta server software
Minecraft beta multiplayer support is currently under heavy development, and is riddled with bugs. You can help test it, though. It will get better soon, I promise!
If you’re running on windows and just want to set up a server easily, download Minecraft_Server.exe, place it anywhere you want, then run it.
If you want to run the server on any other OS, or want to run it without the gui, it’s a bit more involved.
First, make sure you can use java from the command line. On linux and mac, this should automatically work, but on windows you might want to set up a PATH system variable.
Then download minecraft_server.jar to anywhere, then launch it as:
java -Xmx1024M -Xms1024M -jar minecraft_server.jar nogui