I get asked this a lot, as if the question was about two different charts. The Billboard charts are based on Nielsen Soundscan data, so it's actually the same thing.
With that said, the Soundscan situation is a lesson in barriers to entry. Because basically, if you want your album sales on those charts, you better get signed to a label -- and you don't want that.
Soundscan works through an international system of reporters. Every time someone buys your CD in a retail store, that's getting recorded and passed on to Nielsen. (The same company that does TV ratings, yes.) Not every store reports to Soundscan -- Nielsen are lazy fuckers, after all -- and of course, the list of which stores DO make reports is a closely guarded secret. Apparently there's over 14,000 names on it.
When major acts are selling CDs on tour, they're submitting a form to Nielsen where they're reporting the number of albums sold, and the venue is signing off on the document to validate those numbers.
In order to submit that form, though, you need to on a label that's registered with Soundscan, and here, things get tricky. First of all, you need to be in business for over 2 years before you even apply. Second of all, there's an annual fee of $500.
Your CD also needs a UPC code -- not a big issue for most people reading this, but those of you who are up on Revelations 13:16 might object to that. When you order your CDs with Oasis, they include a UPC code.