Everybody can benefit from having good problem solving skills as we all encounter problems on a daily basis. Some of these problems are obviously more severe or complex than others.
It would be wonderful to have the ability to solve all problems efficiently and in a timely fashion without difficulty, unfortunately though there is no one way in which all problems can be solved.
However well prepared we are for problem solving, there is always an element of the unknown. Although planning and structuring will help make the problem solving process more likely to be successful, good judgement and an element of good luck will ultimately determine whether problem solving was a success.
Interpersonal relationships fail and businesses fail because of poor problem solving.
This is often due to either problems not being recognised or being recognised but not being dealt with appropriately.
Problem solving skills are highly sought after by employers as many companies rely on their employees to identify and solve problems.
A lot of the work in problem solving involves understanding what the underlying issues of the problem really are - not the symptoms. Dealing with a customer complaint may be seen as a problem that needs to be solved, and it's almost certainly a good idea to do so. The employee dealing with the complaint should be asking what has caused the customer to complain in the first place, if the cause of the complaint can be eliminated then the problem is solved.
In order to be effective at problem solving you are likely to need some other key skills, which include:

• Creativity. Problems are usually solved either intuitively or systematically. Intuition is used when no new knowledge is needed - you know enough to be able to make a quick decision and solve the problem, or you use common sense or experience to solve the problem. More complex problems or problems that you have not experienced before will likely require a more systematic and logical approach to solve, and for these you will need to use creative thinking.
• Researching Skills. Defining and solving problems often requires you to do some research: this may be a simple Google search or a more rigorous research project. 
• Team Working. Many problems are best defined and solved with the input of other people. Team working may sound like a 'work thing' but it is just as important at home and school as well as in the workplace. 
• Emotional Intelligence. It is worth considering the impact that a problem and/or its solution has on you and other people. Emotional intelligence, the ability to recognise the emotions of yourself and others, will help guide you to an appropriate solution. 
• Risk Management. Solving a problem involves a certain amount of risk - this risk needs to be weighed up against not solving the problem. 
• Decision Making. Problem solving and decision making are closely related skills, and making a decision is an important part of the problem solving process as you will often be faced with various options and alternatives. 

The measure of success is not whether you have a tough problem to deal with, but whether it is the same problem you had last year.
John Foster Dulles, Former US Secretary of State.
What is a Problem?
The Concise Oxford Dictionary (1995) defines a problem as:
“A doubtful or difficult matter requiring a solution”
and
“Something hard to understand or accomplish or deal with.”
It is worth also considering our own view of what a problem is.
We are constantly exposed to opportunities in life, at work, at school and at home. However many opportunities are missed or not taken full advantage of. Often we are unsure how to take advantage of an opportunity and create barriers - reasons why we can't take advantage. These barriers can turn a potentially positive situation into a negative one, a problem.
Are we missing the 'big problem'? It is human nature to notice and focus on small, easy to solve problems but much harder to work on the big problems that may be causing some of the smaller ones.

• It's useful to consider the following questions when faced with a problem.
• Is the problem real or perceived?
• Is this problem really an opportunity?
• Does the problem need solving?
• All problems have two features in common: goals and barriers.

Goals

• Problems involve setting out to achieve some objective or desired state of affairs and can include avoiding a situation or event.
• Goals can be anything that you wish to achieve, or where you want to be. If you are hungry then your goal is probably to eat something. If you are the head of an organisation (CEO), then your main goal may be to maximise profits and this main goal may need to be split into numerous sub-goals in order to fulfil the ultimate aim of increasing profits.

Barriers

• If there were no barriers in the way of achieving a goal, then there would be no problem.  Problem solving involves overcoming the barriers or obstacles that prevent the immediate achievement of goals.
• Following our examples above, if you feel hungry then your goal is to eat. A barrier to this may be that you have no food available - so you take a trip to the supermarket and buy some food, removing the barrier and thus solving the problem. Of course for the CEO wanting to increase profits there may be many more barriers preventing the goal from being reached. The CEO needs to attempt to recognise these barriers and remove them or find other ways to achieve the goals of the organisation.
• The approach referred to is generally designed for problem solving in an organisation or group context, but can also be easily adapted to work at an individual level at home or in education.
• Trying to solve a complex problem alone however can be a mistake. The old adage "A problem shared is a problem halved" is sound advice.
• Talking to others about problems is not only therapeutic but can help you see things from a different point of view, opening up more potential solutions.

Stages of Problem Solving
Effective problem solving usually involves working through a number of steps or stages, such as those outlined below.
Problem Identification:

• This stage involves: detecting and recognising that there is a problem; identifying the nature of the problem; defining the problem.
• The first phase of problem solving may sound obvious but often requires more thought and analysis. Identifying a problem can be a difficult task in itself. Is there a problem at all? What is the nature of the problem, are there in fact numerous problems? How can the problem be best defined? By spending some time defining the problem you will not only understand it more clearly yourself but be able to communicate its nature to others, which leads to the second phase.

Structuring the Problem:

• This stage involves: a period of observation, careful inspection, fact-finding and developing a clear picture of the problem.
• Following on from problem identification, structuring the problem is all about gaining more information about the problem and increasing understanding. This phase is all about fact finding and analysis, building a more comprehensive picture of both the goal(s) and the barrier(s). This stage may not be necessary for very simple problems but is essential for problems of a more complex nature.

Looking for Possible Solutions:

• During this stage you will generate a range of possible courses of action, but with little attempt to evaluate them at this stage.
• From the information gathered in the first two phases of the problem solving framework it is now time to start thinking about possible solutions to the identified problem. In a group situation this stage is often carried out as a brain-storming session, letting each person in the group express their views on possible solutions (or part solutions). In organisations different people will have different expertise in different areas and it is useful, therefore, to hear the views of each concerned party.

Making a Decision:

• This stage involves careful analysis of the different possible courses of action and then selecting the best solution for implementation.
• This is perhaps the most complex part of the problem solving process. Following on from the previous step it is now time to look at each potential solution and carefully analyse it. Some solutions may not be possible, due to other problems like time constraints or budgets. It is important at this stage to also consider what might happen if nothing was done to solve the problem - sometimes trying to solve a problem that leads to many more problems requires some very creative thinking and innovative ideas.
• Finally, make a decision on which course of action to take - decision making is an important skill in itself.
• This stage involves accepting and carrying out the chosen course of action.
• Implementation means acting on the chosen solution. During implementation more problems may arise especially if identification or structuring of the original problem was not carried out fully.

Monitoring/Seeking Feedback:

• The last stage is about reviewing the outcomes of problem solving over a period of time, including seeking feedback as to the success of the outcomes of the chosen solution.
• The final stage of problem solving is concerned with checking that the process was successful. This can be achieved by monitoring and gaining feedback from people affected by any changes that occurred. It is good practice to keep a record of outcomes and any additional problems that occurred.