I have always used a set of alignment bars from Brownells. Turn the flat ends toward each other and make sure the two faces are aligned and parallel. Using the pointed ends doesn't really get you very much precision as both rings can still be twisted but pointing to the same point in space.
Once you get the rings aligned with the bar, gently set the scope in place. Check the 4 places where the tube meets the rings. They should be even and parallel. If not, more tweaking is needed. DO NOT crank the ring caps down until the scope fits in the ring bottoms perfectly. You can bend it very easily. Using this method, I've never found the need to lap. Of course, that may be needed if your receiver is not drilled straight.
As as far as lapping without a kit: I wouldn't try it. I think it would be nearly impossible to freehand the material removal without simply making the whole set up loose.