After looking in the forums a little, I've found out how to get Pico-8--but it's not really clear, so I figured I'd put it down in a forum post for anyone looking through Google.

TO ACQUIRE A PICO-8 FANTASY GAMING CONSOLE:

Step 1: Go buy Voxatron.
Step 2: Give it a minute or so. You'll need to let the payments process and such.
Step 3: You will be able to request a download link for the PICO-8 FANTASY GAMING CONSOLE from your MY GAMES tab.
Step 4: Download and start making games!

Original post, for posterity:

I think it's currently invitation only. I received my invite via twitter

Oh, is it? Doggone it, I saw something in the "Hello World" post that mentioned that Voxatron owners would have it...

If you own voxatron you can just go to the my games page and request a link to be sent to your email address

Okay then. I'll edit the main post to make sure the instructions are accurate.
Thanks for your help!

Would someone invite me so I can make some games?

This post is out of date now. There's no invite process at this point; if you own Voxatron, you have access to PICO 8 as a free download. If you don't own Voxatron and want to get at PICO 8, the thing to do is buy Voxatron.