How do I go about sueing a teacher or school for negligence

You sue a school or teacher--you would name both, in this case: the teacher as the one who did this, the school as her employer--the same way you sue anyone else: by filing a lawsuit in county court. However, this is very much not a case that you could clearly win--there are real challenges in it--and is likely not a case you even want to bring:
1) First, you'd have to prove that this was a deliberate act to humiliate or harm your son. The reason is, based on what you write, your son did not suffer physical injury or harm; when there is no physical injury, etc. there is almost *never* any claim for emotional harm unless there was an intention to cause such harm. The law does not give you compensation for claimed purely emotional harm in negligence/careless cases. (For good reason: since emotional harm is subjective and so easy to claim, if you could sue for emotional harm whenever another person was in any way careless, society would be drowning in lawsuits.) 
However, you'd have to show again that this was a deliberate attempt to cause harm, shame your son, etc., and not that the teacher had some other reason to do this, such as class discipline, or the fact that your son was trying to leave during an important part of the lesson, or that you son had not asked the teacher properly to go but just gotten up, etc. That's not to say that this might not be a case where the teacher essentially "bullied" your son, but *proving* that, if the teacher has some reasonable explanation, may be difficult.
2) Even if you can show that the teacher acted improperly, proving "damages" can be very difficult unless this has resulted in your son seeking therapy or counseling due to this and  you have the therapist testify. Just saying that your son is "embarressed" or does not want to go to school does not by itself show that he suffered any significant compensible harm: children frequently have bad experiences at school, get embarrassed, don't want to go to school, etc. (I have two daughters myself: both have had bad or very bad days in school and not wanted to return.) Just saying your son was embarrassed will not itself result in compensation....but hiring a therapist, having him/her testify, etc. will itself cost money and eat into what you could recover, even if you can prove compensible harm.
3) Finally, do you want to put your son on the witness stand, in court, and have him testify under oath, in front of strangers, that he messed himself in class? And have to answer pointed questions from the school's attorney about this? Because to bring the case, that's what you'd have to do--he is the only witness for your side, and there is no case without him. But the case will be public record, and this will likely get around your district and town.