What is the best way to deal with a coworker who is being disrespectful to me in the workplace?

If the disrespect shown has become more of a habit - the best solution is to take it to the HR Department through your boss for disciplinary action. The least which can be expected of a professional is respect and if somebody doesn't understand that - he/ she needs to be asked to understand!

If you're the immediate Superior give DA with SALARY DEDUCTION . Never tolerate abusive behaviour.

The best way is to first address the problem directly in a decent manner with the person.If this does not solve the problem then you should report it to your reporting manager and ask them to please address the problem using the correct channels, ie.. using HR.

open new page with him/ her and forget the past ... past is past make new friendship with him/her

Thanks 

You need to put limits to him-her by ignoring 

In my opinion, you have to let them know their limits. Talk to them in an assertive manner (not aggressive), tell them that you do not accept this kind of behavior or disrespect, mention that you will take action if this continues (the action depends on your company policies and where you live). You have to be ready to take action if you threaten them with it.

Good luck

Communication, if it does not work then let HR department communicate with him/her. They will make it done for you.