A phone is the most informative object at most modern scenes and the easiest to destroy by handling it. Almost every mistake made with one is made by somebody trying to be helpful.
Record the state you found it in, before anything else. On or off. Locked or unlocked. What is on the screen. Battery level. Whether it is plugged in. Whether it is in a network. These facts stop being knowable the moment anyone touches it.
Do not browse it. Opening a message marks it read, moves it, and changes timestamps that an examiner would otherwise have used. A photograph of a screen you have swiped through is a photograph of an exhibit you have altered — and you will be asked, under oath, what else you looked at.
Do not switch it on to "check something". A device powering up can run scheduled tasks, sync, and apply a remote instruction.
Isolate it from the network. A device that stays connected can be wiped remotely while it sits in an evidence bag. Flight mode where the device is already unlocked and policy allows, or a shielded bag; note which was done and when.
Keep it powered where it was powered. Volatile memory is lost on shutdown, and a device that runs flat may re-encrypt on next boot. Battery and cable go with it.
Passcodes are not guessed. Attempts count towards a wipe on many devices. If someone offers a code, record who gave it and when.
Source. UNODC, Crime scene and physical evidence awareness for non-forensic personnel, https://www.unodc.org/documents/scientific/Crime_scene_awareness__Ebook.pdf ; NIST Organization of Scientific Area Committees for Forensic Science, https://www.nist.gov/osac
What this is not. Forensic examination, which is done by qualified examiners on imaged copies with tools that leave the original unchanged. This page is about the first ten minutes, before any of that is possible.