How do I kill zombies in Minecraft and not get hurt?

Another method is to use a lighter, and ignite the ground while running backwards. It is less risky (provided you're outside setting fire to grass, not inside your wooden house!).

The monsters run into the fire and ignite.

Hitting them while backing up is pretty effective. Just hold your left mouse button button down with your chrosshairs pointed at the mob. When it turns red (indicating it took damage), immediately back up. Repeat until the zombie is dead.

Build a trap! That way you don't even have to waste materials in producing swords, etc. The simplest is to dig a pit 3-4 blocks deep and at least 2x2 wide, and plant some cacti in it. Put the pit between you and the zombie and watch it fall inside and eventually die.

Better traps, such as most water traps, can actually kill the zombie and deliver the dropped goods outside to you. There are many videos on youtube that demonstrate how to build one, (such as this one: