According to the GenArts FAQ section, they say this to register the software:
How do I activate my license?
If the software is already on your machine:
On Windows, go to: Start -> All Programs -> wondertouch -> particleIllusion 3.0 -> Install Serial Number.
On Mac, go to: /Applications/wondertouch/particleIllusion 3.0/Install Serial Number.
Follow the instructions and select the option to authorize over the web. Click here if your machine is not connected to the Internet. If the software is not on your machine, go to: http://www.genarts.com/support/downloads/particleillusion/standalone. Click on the link to download the installer. Follow the instructions and choose the option to authorize over the Internet.