The method I am most fond of is to try to be more interested in the person. Try to find things about the person which you like enough to discuss. Ask lots of questions about the person, but try to avoid subjects that are insulting or painful for either of you. Examples:
How are you? How are your kids? How is your husband/wife/daughter/son? How is work going? How was your weekend? Do you have any fun plans this weekend? How is your week going?
If you have difficulty finding anything you would like to know about the person, you can try talking about a subject with which you both are familiar. Finding common ground is an easy way to form a bond with someone, and will give you more interesting things to discuss. Examples:
Have you seen (TV show/film that you have seen)? Did you see the game/match between (teams you like to watch)?
Finally, try not to be unnecessarily judgmental. If you get a lot of negative feelings toward a person, it will be more difficult for you to have conversations with them. Also, try not to use the word boring. The world is more interesting than you might think, and to call anything boring is to deny yourself the joy of discovering what is interesting about it.
If you find it very difficult in general to be interested in people or your surroundings, consider the possibility of depression. Lack of interest in (or inability to enjoy) the world around you is a symptom of depression, and may need to be addressed by your primary doctor or a specialist.