Often helps to draw a sketch of the physical system, even of trivial
situations or where geometry has little importance.  Sketching may
help remind you of important factors to consider.  When you begin to
define parameters, key them to the sketch if possible.

UG problem sets often emphasized situations where one can write down a
few basic formulae or relations, and then solve the problem
mathematically by formal manipulation.  Most "real" problems in this
course emphasize physical reasoning instead.  Formal manipulation
without physical insight will rarely get you the right answer.

Many parameters enter problems in this course, even if in simple ways.
Be careful in defining them---it helps to write out the definition of
each.  Use clear, consistent, complete, and unambiguous notation.  

Neatness, of a sort, actually counts, other things being equal.  The
more carefully you write and organize your work, the more likely you
are to do it right the first time or recognize where there may be
problems (e.g. numerical errors) the second time.  

Solve problems conceptually before starting to plug in numbers.  Break
the problem down into its key steps.  Show the logic of the argument.
Write out clear algebraic solutions, again by steps.  

Rather than putting everything into one large and unwieldy expression
(which lends itself to numerical errors when evaluated), define
symbols for intermediary quantities and write out albegraic
expressions for these.  Then, solve the expressions and give numerical
values for important intermediaries.  Perform a reality check on each
of these before proceeding.  

Always give the units of any numerical answer and double check that
they are as expected.  Being careful about units in intermediate steps
often prevents confusion or error in getting the final answer.

Despite the adoption of SI units in physics, astronomers nearly
universally still use cgs-based units.  Don't fight this.  Convert to
cgs/astro-units at the beginning of the calculation and use those
units exclusively throughout.  Using mixed units or trying to
convert at the end of a calculation can lead to dumb mistakes.