The short answer is they didn't ever say.

The long answer is we can use what we know plus logic to speculate on possible answers. The answer I've settled on personally is that he knows how to consciously increase or decrease his own souls "pull" on other souls allowing him to overpower the last dragonborn's. As for how he does it when the dragon is still living is less clear but there are still a few possibilities. The only thing we know for certain about that is that it isn't a shout.

How he heals with them is the same sort of thing. He has likely learned to convert the energy into life\healing.

All of these things the last dragonborn could learn to do in time.