The first method is Apple's own 'Move to iOS' app. You can download the first-party service on Google's Play store for free and use it to transfer contacts, photos and videos, and more.
Note: In order for the service to work, you'll have to be in the iOS Setup Assistant, which is the start-up page when you first turn on your new iPhone. If you've already set up the device, look to the second method in this guide.
1. Once 'Move to iOS' is installed, accept the terms and conditions, and allow the application to access your Android phone's location.
2. You will then be asked to Find Your Code. Tap Continue. From your iPhone, follow through the Setup Assistant until you see Move Data from Android.
3. Enter the six or ten-digit code from the iPhone into the Android. A Transfer Data screen will appear, with a list of items you can copy over to your iPhone. If you're just moving your contacts, check off the respective bullet. If you want to move all of your files and data, check off everything.
4. Leave your Android and iPhone untouched while the transfer is processing. Depending on how much you're moving from phone to phone, it can take as long as 30 minutes.
More: How to transfer your number to Apple's newest iPhone