It depends on the item you are requesting and which libraries own it:
If you request an article from a journal/newspaper/magazine that many libraries own, it could take only a few hours or a few days for it to arrive in your ILLiad account for download. If not many libraries own the item, it will take a little bit longer -- usually not longer than one week.
If you are requesting a book, several variables influence when it will arrive:
We first ask libraries that are geographically close to us to send us a book -- that usually takes anywhere from 3-7 business days.
If the book is only available in a library far away, it could take anywhere from a full week to 2-3 weeks for it to arrive.