What is the most important part in solving a math problem?

I think this depends on the kind of problem being solved,
so I will address word problems in particular, with some additional comments on math
problems in general.  It might be fair to say that everything is important in solving
math problems!

If a word problem is being solved, the most
important aspect is creating an equation with the numbers and concepts in expressed in
the problem.  Words in the problem must represent a mathematical operation or the
problem cannot be solved.  For example, if one is told that a number is three times
another number, the word "times" tells us that a muliplication is involved.  Another
example is the word "less," when one number is two less than another number.  The word
"less" tells us there is a subtraction involved.  As people practice with this kind of
problem, the "translation" from words to operations gets much
easier.

Assuming that an equation already exists, it is my
opinion that the most important part of solving a math problem is writing down every
single step.  Many people find it easy to do the steps in their minds, but if something
goes wrong along the way, there is no way to figure out where it has gone wrong unless
each step is written down.   I remember that when I took calculus in college, we were
given homework problems that involved pages and pages of calculations.  If I did not
write every single step, I cost myself hours of
work.

Another aspect of doing math that is quite important
is checking your answer.   All equations can be proved by simply plugging the answer(s)
into the equation for the variable(s) being sought.  Quite often I find that students
have used the correct method and have made some trivial arithmetic error that could have
been caught by this method.