First, please verify that the video is in your camera roll.
Then, Open the YouTube app on your iOS device. If you do not have the YouTube app, it can be downloaded for free from the App Store.
Tap on the little camera located on top-right corner (circled below in red).
On the next screen, locate your video and tap on it.
Follow the on-screen instructions. When finished, tap “Upload” on the top right corner of your screen as shown below.
YouTube will process your video. This can take a while: for example, a 1-minute video can take over 10 minutes to process. Once processed, the video will appear on the “My Videos” screen, which can be reached by tapping on the “Library” tab at the bottom, then on the “My Videos” menu.