When the drone is flying is it recording video the whole time or is there something I need to do to stop and start the recorder? I can't seem to find the answer in the beginnger videos.

Push the button on screen to start. Push again to stop.    It's all in the manual.

Hey there, if it is in recording mode. you can tap the round circle to start or stop recording video. More details, please visit the user manual.
https://dl.djicdn.com/downloads/phantom_3_standard/20170623/Phantom+3+Standard+User+Manual+v1.4.pdf

1) be sure you are in video mode 2) press the round red button on right side of screen 3) Listen for audio confirmation tht recording has started. It's just a muted chime. 4) Look for visual confirmation in that the circle is now a square plus you should see a digital log of lapsed recording time. Not always easy to see in the sun so look for the square. 5) press again to stop, As mentioned, read the manual for details reagarding settings, etc.

It's good to read the manual.

It's only recording if you turn on the recorder by pushing the button on the right side of the DJI go app, kind of like a camcorder, it will also beep and show the recording time.  Otherwise, no it isn't recording.