what is the most important principal that you need to be acquainted with while you are dealing with the problem solving mechanism ?

Every individual has his/her own way of dealing this, this is my way 1.I always remember that problems are inevitable and the learning curve is high and fast when you solve it 2.Never get overwhelmed and be calm 3.Asses your situation and put a priority to each of them 4.Delegate whatever you could however you should have a good ping back strategy 5.Lastly, use the divide and conquer.
Ensure that you separate the problems and deal with it individually 6.
Make yourselves transparent especially the communication part.
Once this is established people are aware of what you are and many problems seem to vanish without a trace...
Cheers, Sudhish

Calm Down , Listen , Think , Smile , Suggest , Help !

Actually I'm using 2 ways, each one for the suitable situation: 1-"PDCA" technique, thus are action that you should by this sequence, "Plan" how you could solve this problem by all of ways (the current situation and to guarantee that this will not repeated again.
Then "Do" execute your ideas , your solution, in the real field.
After that "Check" what did you do, did it meet my goals, my plan, solve the problems, the percentage of success, and seek for the feedback, follow with your internal and external customer.
then start to take "Action" to points that you get from check step, we called corrective action and you have to follow up and make continues improvmets
2- "DMAIC" this technique is from six segma way of improvment, and could be used in product or service, DMAIC stands for:
1- D: Define, In product they say if you make will define to your problem, you solved the problem by 80%, and in sevice by 50 %.

2- M: Measure, you have to measure the problem and its effect and how many it repeated, but here there is a very important thing that you have to select the proper KPI (Key Performance Indecator) 3-A: Analysis this is that make you see the picture after both of first to thing and go deep by you measurment to see the effect the meaning of this number ask why, after this step you should be able to know the root cause of the problem.

4- I: Improve: start know make a suitable solution to improve and implement it.

5- C: Control : you have to see what happen after your implementatin if it is improved or not , and start to put it on the line