This tutorial will learn you how to be a real lumberjack.
If you follow all of these steps carefully there's almost no risk to get hurt. And, if you'll get hurt when splitting logs, I'm not responsible for it.
UPDATE: Please read the comments in the bottom of the page, though these provide information on how to cut wood in a better and safer way.
Step 1: What you'll need
So, here's the list of things you need for doing this:
An AXE - Sharp, not too small, not too heavy.
A LOG - Dry, it's easier if it's quite small. If you got big logs read the part "Splitting big logs"
A STUB - Or something else to put under your log. It should be stable. The good thing with having a stub is that the axe doesn't get hurt if you fail to hit the log.
A SLEDGEHAMMER - May be good if the axe is stuck.
SAFETY GOGGLES - Good for the safety.
A FRIEND - Safe
If you got long logs you'll also need:
A SAW - To make shorter parts, like one foot (~30 cm) long.
A SAW BUCK - Or something else to hold the long logs with when you saw them