Hi, I'm a newbie too, and I had a similar problem doing a tutorial a few days ago. In the options for the split polygon tool, do you have snap to edge turned on? If you turn it off, you can make the inbetween vertices which aren't on the edge, and turn it back on again to make the last vertex at the edge, and then complete your split by pressing enter. Another handy tip is that you can click and drag with the middle mouse button to move a vertex you've just made.