You can buy a registration key online using a credit card or PayPal from the Expert Sleepers Licence Manager application. See here for more information.
The e-commerce side of things is handled by eSellerate. If you have any security concerns, have a look at their website which is pretty informative.
Your registration key allows you to install Crossfade Loop Synth on up to 3 different computers (useful if for example you have a PowerMac in the studio and a laptop for live use). You will need to be connected to the internet for the product activation to work effectively.