The same subject in the same background shot from two different angles would result in two completely different looking portrait photographs.  Choosing the best angle to shoot a portrait photograph is crucial to the final look of the portrait.  

Here are some tips that will help you select the right angle for your photograph

Direct shot

This means that you shoot the subject directly from the front at about the nose or eye level.  It will give you portraits with the subject looking directly at the camera.  These are ideal for conventional studio portraits.  Also remember that direct shots work best when you are shooting a waist-and-above or shoulders-and-above portrait as opposed to full-length portraits.
    

High shot

This would require you to shoot the subject from a higher angle, i.e., the subject would be looking up at you.  Most selfies are shot from a high angle.  You can experiment with different angles from a higher point to see what looks best.  Keep in mind the body type of the subject.  If your subject has a long neck, avoid shooting from above as looking up would make their neck look longer.
    

Low shot

This is shooting your subject from a low angle so that they are looking down at the camera.  As in a high shot, you can try out different looks from this angle, keeping in mind what looks good on your subject.  Do not get a subject with a double chin to look down into the camera, it will amplify the heavy chin and make them look bloated.
    

Side shot

Shooting your subject from the sides gives you a lot of scope to experiment.  Try out a high or low side angle or get a side profile portrait.  The options are plenty.  Play around with the light when shooting from side angles and you could get some unique and stunning portraits.
    

Action shot

When shooting action portraits (children running on the beach or a teenager shooting a basketball) try out different angles.  You will often shoot these from a distance and a low angle or a direct height shot would work well.  Also keep in mind the angle of light in these portraits as your subject is moving and you need to avoid shadows.

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