For the test I will be using a six (6) inch oak log, and a knife with a four (4) inch blade. The log was cut using the modified Trail Blazer 24 inch Take Down Buck Saw.
The first thing you need to do is find a strong stick and sharpen one end into a wedge. Here I am using oak as well. The harder the wood you are using for the wedge, the better (it will need less re-sharpening). You want the stick to be fairly long, so it can get the job done in case the wood is stubborn.
Use the knife and a baton to make a notch in the log.
Then take the wedge, and start batoning it into the notch that you made. The wedge should go towards the edge of the log, not the middle. If you try to baton it through the middle, the job will be much harder. This is the same technique you would use when splitting wood with a small axe-aim for the edge of the log rather than the center.
This part can take a lot of work. I had to spend about fifteen (15) minutes batoning (including the time I had to stop the re-sharpen the wedge. Eventually, I started to get a crack down the side of the log.
When that happened, I put the log on its side, and placed the wedge in the spit and continued batoning.
After a few more hits, the wood was split.
This was a very energy and time consuming process. I am sure some woods can be split a lot more easily, but while doable, this is not a practical method for splitting significant amounts of wood. If I had to use this method to gather a pile of wood that would last me through a winter night, I would have to spend the whole day splitting.
In the alternative, you could just bring the right tool for the job, and get the job done with one swing (review is on its way).