Left-clicking places a block. Right-clicking destroys a block.
Blocks cannot be placed past the existing border.
Falling off the edge or digging through the bottom of the world will not kill the player.
Changes
Blocks
Block types are handled depending upon where they are located within the world, as opposed to later versions where any block can be placed anywhere. Blocks at the same level as grass turn to grass and blocks at the same level as cobblestone or air turn to cobblestone.
World generation
Level generation improved to be not so messy and random (as shown in the Cave game tech test video), but instead completely flat.
Trivia
This is the oldest version of Classic in the launcher, listed as old_alpha rd-132211. It is also the earliest found version of Minecraft.
The 'rd' before the version number stands for RubyDung, a game Notch was working on.
Holding down R causes the player to rapidly cycle through respawn locations above the level until it is released.