How can I get my pictures and Apps off my old iPhone into my new one?

Transfer Data from old iPhone to new- (You did not tell us anything about your old iPhone so I am going to assume that it will work with the methods listed below)

Do you have a backup created either on iCloud or on your computer?

Method 1 - Backup your old iPhone on your computer like this -->>How to back up your iPhone, iPad, and iPod touch - Apple Support and then Restore your new iPhone from that backup like this-->>Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Method 2 - The Quick Start method and here is how to do that-->>Use Quick Start to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

Do you have your old phone? And it powers up?

Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support