So I just paid my membership to the jade club, and I see this button that says "Register your Puzzles" Does anyone know what I do here?

jade puzzles have a chip inside, you will receive them with a numerical code associated with chip.
with this button you can register these codes...
what is all this? an old project of JC, i think it's now abandoned

Also, how long would it take to get the jade cube and pyraminx?

You may not get them at all. At least that is what happened in my case. I paid the Jade club membership fee in December of 2010. Wrote several times to support@mefferts.com (in January, March and April 2011) to hear where my "Free Jade Pyraminx" was.

To date I have received no reply from Meffert's, and I've given up trying. Because of this, I've also refrained from buying anything from Meffert's since then.

I do hope, however, that you'll have more luck.

I had the same experience as Taus, however a quick email to the Jade Club email and it arrived at my door shortly after.