First and foremost, it's important to remember that creativity requires time. The movie-making process is not a fast one, but learning is both deep and engaging. Think about how much time you're willing to spend on a video project, and help your students set realistic goals for that timeframe. It's time worth spending--just think about how video can amplify student voices!
Nikon does a great job giving an overview of moviemaking, but I also have some tips of my own.
Check the Audio
Will you record your audio as you go or record a voiceover?
Where's your device's microphone? Is there any possibility of accidentally covering it?
Stabilize the Shot
Do you have a tripod you can use?
Can you use your body or an object to stabilize your device?