My technique for splitting kindling from 4" square down to around 1/4" (or even 1/16" when the grain is straight enough) is pretty much as Schwert and Chris described.
I have some chopping blocks; pieces of trunk, between 18" and 30" in diameter, about 2/3 of that in length, stood on end.
I take a piece of wood that I want to split, and place it on end on the block and place the hatchet on this piece.
Now I give a little whack with the heel of my left hand on the back of the hatchet so it bites a little into the wood.
Or, if the piece is too uneven to stand, I lift the piece with the axe, and tap the two together against the block.
This gets the edge into the wood, by about 1/4", enough to lift the piece of wood with the hatchet and bring them down smartly. Whack!
This way, my hand is never below the level of the edge while the hatchet is moving.
You can do it sitting down, if your block is too low and your back starts to ache.
This technique is efficient and fast. I can make enough kindling in five minutes to light the kitchen stove and living room fire three times over.
Keith.