I was in this same situation before I opted for the lathe instead of the bandsaw. If you search these forums, there are some good discussions about resawing on a table saw.
I have a bunch of 2x stock, mostly 2x6, that I was working with, and wanted to resaw it to about 3/4". I did it a few times with push sticks, but it was pretty nerve wracking, so I made a jig that kept my hands well away from the blade, but still gave me two multidimensional control over the piece that I was cutting.
But for basic how-to, I'd set the cutting depth to about half the width of the board to be resawn, set my fence to cut for the thickness that I needed, then made the first cut. Then, I'd flip the board end over end so that the same side is against the fence and make the second cut. I tried to leave about 1/8" in the middle so the pieces didn't fall away from each other after the second cut (possibly binding the blade). Then I'd pop them apart. I'd use a block plane to take the nub off the middle, then run it through my planer for final thickness, or you could just sand it to clean up the blade marks.
Final remarks - if you resaw on your tablesaw, keep your hands as far away from the cutting area as possible. Make a jig, use featherboards, push sticks, whatever you can to stay plenty clear.
I'll post a pic of my jig when I can.