Hi Folks! Welcome to my first Instructable!
First of all, this method was not originally my idea. I noticed that there was not an Instructable on this subject, and I decided to make one. Feel free to leave tips, suggestions, or questions in the comment section.
This technique is known as Batoning, and it is most useful (in my experience) when splitting thin pieces of wood for kindling, or for when the surface you are splitting on is not completely level.
From Wikipedia: This technique is useful for the simple splitting of wood for kindling, to access dry wood within a wet log, and for the production of shingles, slats, or boards. It is also useful for cutting notches, or making clean crosscuts against the grain of the wood. Batoning requires much less energy to perform than chopping, which is helpful in survival situations where energy should be conserved. The technique is also especially useful when a chopping tool is not available.

Step 1: Gather Materials

Safety First:
Eye Protection

Work Gloves (I'm not using gloves because it was hard to work the camera with gloves on)

Sturdy Shoes

Splitting wood can be a dangerous activity. I am not responsible for any injury to yourself or others as a result of this method. Be Careful.

A stump/sturdy surface

A log to use as a club/hammer
Should be easy to hold and swing with one hand

A fixed-blade knife
The knife you use should have a thick spine, and a grippy/secure handle.
Do not use a kitchen knife; do not use a folding knife. Both will probably break.
The blade of the knife needs to be longer than the diameter of what you intend to split
Warning: There is the potential that the blade of your knife will break off into the log. I have never had this happen to me, but just beware.

Wood to split: Should be cut to size to use in a fire.

Step 2: Positioning the Log

Select a piece of wood you wish to split.
If you can, stand the piece of wood vertically upright on the stump/platform you are using. If not, hold the piece of wood upright in you right hand and press down on the wood with your knife in your left hand, so that it doesn't fall over. You can then remove your right hand and retrieve your club.

Note: You want to be holding the knife in your non-dominant hand. If you’re left handed, hold the knife in your right hand and the club in your left hand.

Step 3: Splitting the Log

Tap the spine of the knife with the to get it firmly lodged in the log. Once it is lodged hit the spine of the knife again with a series of hard swings until the spine in below the top of the log. Now, hit the tip of the knife repeatedly until the log splits. You can continue doing this with each log half that you split to get pieces small enough to use as kindling.

Step 4: Tips and Troubleshooting

Firmly press down on the handle of the knife as you are splitting. This will help keep the tip of the blade traveling farther than the handle. If this does happen, hold the log at the top in your hand press down on the handle to attempt to even it out. If that doesn't work, hold the log at the top in your hand and hit the handle of the knife with enough force to make the blade and handle even.