According to this post on the Multiwinia forums, the beta sign up is commencing, with folks being signed up in batches of fifty. Chris says:
We will start the process soon with a small number (around 50) of testers running a non-playable "Hardware Test" build. This build will pit 4 AI players against each other and will report back to us with frame rates, hardware stats, problems etc. During this phase we're looking at hardware compatibility problems, frame rate issues etc. After this we'll start rolling out playable versions for the testers to break, gradually adding applicants to the test group in batches of 50 or more.
And just in case you missed it, I interviewed Chris and Mark from Introversion a couple of weeks ago.