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
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
Step 2: Safety
- Don't do like the man in the first image... quite obvious.
- Use SAFETY GOGGLES
- Stand with your feet separated, not togehter, because otherwise, if you miss the log with the axe, the a will hit your legs instead. Not good. At all.
- Be two, like in all extreme sports. If you hurt yourself your friend can help you. BUT, the friend shall be at least 10 feet away from you
- Stand on a level surface
- Use a sharp-edged axe. If you don't, you have to use more power. More power - More dangerous.
Step 3: Splitting Small Logs
Do like this:
Put the log on top of the stub, like in the picture. If it is a twig on the log, put it downwards, because if the first thing you hit is a twig (the tree i more solid there), it's harder to split it.
When you have placed the log on the stub, get your axe and aim (by placing the edge on top of the log). Then lift the axe over your head and hit it. Try to hit the middle of the log, so you chop it into two halves that are almost the same size.
Then, if you are pleased with the size, take the next log and do the same thing again.
If you want it bigger: forget it. If you want it smaller: Split it again, but only one piece at the time, NOT both parts.
Step 4: Splitting Large Logs
The idea behind this strategy is: if you chop small things it's easy, so chopping small pieces many times is often easier.
Remember: Always aim before you hit.
If you tries to chop the log, and the axe get stuck, use the sledgehammer to beat it through.