Modern phones have video cameras that are up to the task, but I don't think you'll get acceptable audio quality if you just record directly from your phone.
A lavalier mic that plugs into your phone would be a good investment. See http://www.rode.com/microphones/smartlav-plus for example.
For good video, ensure you are well-lit, and your phone is attached to a tripod or something. You don't want it moving around while you're filming.
You'll find Udemy's official guidance at https://teach.udemy.com/course-creation/set-up-your-filming-studio/