It is obvious to look at somebody when writing to find their most dominant hand, but there are a few ways to find somebodies most dominant hand. One of these ways is that a person will most probably but their mobile phone or wallet on the side of their most dominant hand in their pocket (Mostly Males). I know I always put my phone in my left pocket without even thinking about it however, some people may put phones and wallets in their pocket in which they feel most comfortable. So do not go on this alone, try and find other ways to see which is their more dominant hand by seeing what hand they hold a glass in or what hand they use to answer the phone on to support your answer.
For women, they will usually put their hand bag or carry their bag in their more dominant hand as they will feel more natural, but do not go on this alone. Women will also usually apply make up or other things to their face with their more dominant hand as it is usually the more steady of the two.
Another way to find out is, to look at what foot the person takes their first step on. The balance of probability is that the side of which the foot is first stepped on to is their strongest or most dominant side, therefore it is probably that side of which their strongest hand is on.
In an aggressive or dangerous situation, people with slight knowledge of fighting or self defence will turn so that their strongest side of the body is the furthest away from the person or object in which is dangerous. This is like boxing in which the strongest arm is the furthest away from the opponent, so that the stronger and more critical punches are from their strongest side. This may not be as visible in public but a person will slightly turn their body into this stance unconsciously. It may be just a slight leg movement or just a dropped shoulder which occurs but it is a good way to find a persons strongest side.
Do not take one of these into account, try and find other sources of evidence to back up your answer to try and figure out the most probable of the two arms which is their dominant side. It is good to try this on people you have only just met or people you don’t know very well. I suggest practicing this as often as you can, and you will discover your own ways to identify a persons most dominant hand.
I would like to hear about what you have discovered and other observations you have done to figuring out a persons most dominant side.