If you want to assign a photo (from gallery or camera), there are 2 ways: from Contacts or from Gallery. To add a photo to a contact on iPhone 5s running iOS 9.2 or later, do as follows:
1. Open the Contacts application from the home screen (Or open the Phone and tap the Contacts button in the middle bottom)
2. Find the Contact you want to assign a profile picture to and tap to open it
3. Tap the Edit button on the top right
4. Hit the Add Photo button left to the First and Last name, and specify whether you want to Take Photo or Choose Photo from the Gallery
5. When you select the photo, Move and Scale it to fit the given Frame and hit the Use Photo button in the end
Tip: To delete the contact's photo, go to the Edit menu, tap the Contact's photo and hit the Delete Photo button