I just got a new iPhone because my other one broke & I was wondering how do I get my information (pictures, contacts) transferred back to my new phone? My broken iPhone was backed up... I've done it before but i forgot the steps.
Assuming that you have an iCloud backup since you tagged your question with the "iCloud" tag.
If your old iPhone was backed up via iCloud then you just start the Setup Guide (the thing you see when you first start up an new iPhone) and go through some basics like language and connecting it to your Wi-Fi network. After that you will be asked if you want to set up the phone as A new iPhone, From an iTunes backup or From an iCloud backup. Choose iCloud backup. In the following step you will need to enter your Apple-ID login credentials. After that your iPhone will start downloading the data and it will take care of everything by itself.
The Setup Guide is easy to follow. Just read carefully and follow the instructions.
You have to restore your new iPhone so you can get the "Restore to iCloud BackUp" option, otherwhise you only will get your basic info (Contacts, Notes, App Documnets and Streaming Photos, and all of this if you had them enabled).
So if you want to get the BACKUP into the new phone, restore it first and then you can do this, if you only want data sign in with your iCloud Backup in Settings App.
You may want to take a look into this documentation: https://support.apple.com/kb/ph12521
Hope it helps.