If you don't want any sediment in your beer bottles, then the only way is to buy yourself a filtering system. After you've filtered away all the yeast the only way to get carbonation in the bottles is to artificially carbonate them, so you'll need some equipment for that as well.
If you do decide to do this, you must remember to leave your beer in a
secondary fermenter for quite a long time, since after the yeast gets taken out the beer won't develop at all. And I'm sure you have noticed how the taste gets better when your beer conditions in the bottles for a couple of months.
You must also remember, that aftificially carbonated beer will only stay good in the bottles for a month or two, whereas naturally bottle conditioned beer will usually be good for much longer.
Natural airation? There's no such a thing. I believe the person who has said this meant to say natural carbonation, which is just another term for bottle conditioning.