How do I recover deleted photos and videos on iPhone?

If you don't use iCloud Photos, but you have Settings>Apple ID>iCloud Backup turned on, then you may be able to recover data from the last 30 days or so. You should look here:

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support 

“Restore” is what you do when you buy a new phone, so this safety, if you have it set, requires you to erase everything on your phone and replace it with the backup.

As muguy says, if you don't keep your own backups to an external drive, then there really isn't any place else to look.

Anything in the Recently Deleted album in Photos can be recovered. If your items were further deleted from that album, they were permanently deleted and irrecoverable.