Most countries have laws in place that protect employees. Assuming that your boss is not the owner of the company or the highest level in the company, there should be a Human Resources area that you can take your issues to, or even a Labor Department in the government that can help you.
Having proof of your boss's mistreatment is important, so if there are other co-workers who would be willing to document things they have seen or heard, that would be helpful. In most cases, just working with the company's human resource area, is the best way to resolve the problem. If your boss is breaking employment laws in your country, they can remove him from his position, or, possibly move you to another area.
Please let me know if I can help further.
That is more difficult if your boss owns the company. Your best bet is probably going to be contacting a lawyer in your country that is experienced with employment and labor issues to see what rights you have and what options are available to you other than quitting your job.
Again, most countries have laws in place that protect workers and finding out how those laws can work for you is important. Perhaps if he is mistreating other employees also, something can be done to stop the behavior. You may find that looking for other employment will be the easiest solution to the problem; but again, a lawyer or legal council would be the first step to take if the situation is truly impossible to handle.
If you don't want legal assistance, I would simply make an "appointment" with your employer and let him know exactly how you feel. Tell him that when he yells at you or demeans you, it makes it difficult for you to to do your job well, and that you want to be the best employee you can be. Ask him what you can do yourself to improve your work, what his expectations are for you. Let him know how important your job is to you, and that you want to do the best for him that you can. Ask him if you have discussions with him twice a week for a while until he feels it is no longer necessary. Ask him to make notes of things you can improve on and discuss them with your employer in your meetings. If he doesn't want to meet twice a week, ask for a weekly meeting or whatever he is willing to do.
It's important that he knows you are sincere about doing a good job for him. Some people are naturally 'abrasive' and treat others with less respect than they deserve. This may be a personality issue with him more than anything. Be respectful of him and let him know how his actions make you feel, and let him know that you feel you deserve to be treated as well as you treat him and the other people you have contact with.
This honestly could just be the way this gentlemen was 'taught' to work....and sometimes, as you say, a simple discussion with a list of expectations, is all that is needed to turn things around.