My mother tells me to recite the word "delete" over and over again and picture it leaving my mind. It may seem silly, but visulaization exercises like this can help you refocus your energies on the fact that this is a bad thought, and it's not doing you any good and needs to be gone.
I put things into perspective and evaluate what they really mean in the grand scheme of things. I do this in hopes of realizing just how minimal the situation really is, which will thus help me to strip away the power and influence of the negative emotions.
I also try to look at the 'bright side of things' and find a positive side to whatever is bothering me and hold on to that positive side. For instance, when I first started driving I had 2 wrecks in 9 days. They were both my fault, and I basically did about 3k worth of damage on my sister's car. It was tough, but I chose to focus on the fact that nobody was injured and used that positive point to keep me somewhat calm through it all.
I try to deal with the situation that is causing the negative emotion and see if it is anything that I have control over. If I have any control over the situation then I work to find a solution to the issue. If I have no control over it then I work to control my response to the situation and realize it is out of my realm of control.
Personally, I subscribe to the "Pollyanna" philosophy. I understand that we cannot control what life throws at us, but we can control our response to it. As a teacher, I cannot control the students in my class who refuse to be motivated, but I can control my response to them. Rather than be upset that they don't see a value in education, I can appreciate them for their individual characters. When my mother died unexpectedly during her battle with cancer, I was upset yes, but I knew she was spared the pain and suffering of this debilitating disease.
When negative emotions are not sudden, and instead sort of "creep up on you," one of the best ways to deal with this is to focus the negative energy into something positive. For instance, if there is an argument between friends, or a break up, or a bout of depression, diverting your negativity into something positive is helpful. Finding a new hobby, volunteering, starting to work out or train for a race; these are all opportunities to not only get your mind off of the negative, but create a new atmosphere for yourself.
In a way, you are killing two birds with one stone. Not only are you focusing on something new, therefore not dwelling on the sadness, anger, or grief - you are also getting involved in something new. You will meet new people, or lose weight, or learn a new craft.
All in all, the best way to get rid of the bad is to bring in the good!
That depends on how prepared I am for the emotion to happen. I deal with negative emotions badly if I am surprised by them. When that happens, I tend to lose my temper. I also tend to do stupid things like eating too much when I am stressed.
If I can anticipate what is going to cause me to have negative emotions then I can do much better. What I do then is to rehearse how I will react to the bad things that happen. For example, if I anticipate that a student will say a particular thing about me or my lesson, I have a response ready. What the student says still causes negative emotions, but I have a response ready so I do not have to respond in an emotional way.
One of my favorite ways of handling negative emotion is to remove myself from the trying situation and take the time to exercise for at least an hour. I find that walking away from the thing that is causing the negative emotion is helpful but being able to really process what is happening while running or riding my bike is really helpful in the long term and often helps me find resolution to the problem.
Another way I like to treat negative emotion is to try and make light of it, when appropriate. If I can laugh about what is happening and particularly help the other party involved laugh about it, it often helps to put us on the same level and again lead to resolution.