You might want to look here:
http://pipesmagazine.com/python/pipe-smoking/tobacco-pipe-packing-methods/
At the bottom of the page is a link to the second page, which has videos.
I suspect that the three step method, or some variation, is the most common, though I'm sure that there are many experts who simply stuff and puff.
Even with the videos, there is a certain amount of "feel" to packing a pipe that you get from experience. Not too tight -- the goal is not to cram as much tobacco into the bowl as possible -- but not too loose. When doing the three step method, bear in mind that you want the bottom of the bowl packed a bit looser than the top. That way, as you tamp, the bottom does not become too compressed.
Most use two initial lights. The first, often called the false or charring light, causes some tobacco to rise up in the pipe. You need to gently tamp that down and try to make it even. Then, light the bowl again trying to make sure that you've lit everything evenly.
When you tamp as you smoke, try to even out the top by gently pushing the tobacco and ash from the edge towards the center. The center might even be slightly raised. Don't over analyze what you are doing. It's not neurosurgery. Don't tamp too forcefully. The goal is not to crush the tobacco into the bottom of the bowl. Gently compress and try to straighten out the top. If your pipe goes out -- it happens -- tamp and relight. Again, move the flame so as to try to get an even light.
If your packing does not seem to be working, you will need to experiment a bit. Not having experienced the phenomenon you describe, my guess is that you are packing too firmly? Try packing a bit looser. Of course, if that doesn't improve things, then the obvious thing is to try packing a bit more firmly. Hang in there. Take a look at the videos. That and a bit of trial and error will get you where you need to be.