How do I wipe old iPhone without affecting new iPhone/iCloud?

I got a new iPhone from my wireless provider and I have already transferred all my data from the old iPhone to the new one. In order to trade my old phone in I need to delete the data without affecting the new phone/iCloud. Is there a wrong way to do this? Will I accidentally delete all of my photos, contacts, iMessage history, etc.?

Having two or more devices linked to iCloud can make it confusing to know when and from where you are deleting data. I need all my data to just be on the new iPhone. Thanks.