It should come via email with a link to your LimeWire PRO Download Page. It'll be from "customer@limewire.com". Keep an eye on your trash so you don't delete it by accident. Once you get it, remember to bookmark your d/load page.
Don't know how long it'll take. If you have questions, try sending a PM to
limenathan (click on link). He handles billing questions.
As ZombieGak mentioned, make sure you ordered it from the official site:
http://www.limewire.com/english/content/download.shtml