There are so many different techniques that have been used in the history of cinematography, and many of them are actually ones that are developed by people to solve specific problems or achieve difficult image needs. Here are some cinematography tutorials that will address different techniques you can try to capture moving images.
The specific camera angle is actually where most people begin considering how they want to present a digital video image. There are common video camera angles that people tend to go to because they are part of the lexicon of film language. Look into this cinematography tutorial that outlines the five most important camera angles.
Scenes, especially in the narrative context, are composed of differently positioned cinematographic angles and points of view. This is done to maximize different perspectives, focus points, and to present a physical space for the scene. This can be done by utilizing a master shot and coverage, which are ways of arranging these different shots. These two can also be at odds, so looking into a cinematography tutorial on how to choose between the master shot and individual coverage.
Going handheld can be a very freeing experience for how you get images, but it can also create very difficult shots and few will actually be usable. There are very few situations when a handheld camera image is realistically stable, but it may be the only way to get different angles. Look into a cinematography tutorial with some tips on how to use the handheld approach to get images you want.