I bought a new Mac a few days ago. I did a clean install, so I can start blank. Now I want to restore some files back from Time Machine to the new Mac. Is there a way to get the Time Machine interface so I can travel through my old backups using TM on my new Mac?
To restore the latest backup, connect the drive used for Time Machine to the new Mac and run
/Applications/Utilities/Migration Assistant.app. There is also a support document from Apple covering this (but it reads some reading between the lines because it covers several use cases as once).
To access the backup as a whole, see this answer.