Get All the Shots You Need
Make sure you get all the requisite set-up shots, cut-aways, and so on, even if you don't think you'll use them. They may come in handy in the edit room.
So start with an establishing shot - such as video of the person who is the subject of your story - and then remember to get the other kinds of shots you may use to supplement that in your final film.
The latter is called B-roll, which refers to the earlier days of film when you had two rolls of film - A and B - and you had to edit them together.
A-roll is the main subject of your shot, invariably with audio such as an interview with someone. B-roll is the background video for your film, often just video over which you'll lay an audio track (such as the person talking in the A-roll). So don't forget to shoot a variety of B-roll.
Another type of shot to look for is natural sound (called "nat sound"). This is film that has some natural background noise - traffic on a street, birds chirping in a park, etc. This audio can add depth and impact to a two-dimensional video tape.