How can I recover deleted files after Migration Assistant process on my MacBook Air?

I got a new MacBook air and transfered documents from my old MacBook pro using the Migration process. All the desktop items, email, notes and all browsing history is on the new Mac but now after I delete all files from the old computer and traded it in at apple all my desktop items are gone in the new one but all othere Data is still there. there is nothing in recently delete and I can not find recently deleted files in the Icloud

[Re-Titled by Moderator]

Original Title: File transfer via the migration process