If you want to improve your writing - start a journal or a diary. Every day
put something down, regardless of how trivial or how stupid it may sound.
Some days maybe just a one or two liner, but eventually you will get into a
habit of recording your thoughts, and your entries will become more
elaborate. This is perhaps the most efficient method. Don't try to be
grammatically perfect - but try to be fluent. The "flow" of your writing is
just as important, if not more so, than just form some grammatically
impeccable yet robotic statements.
As to reading sources, I would say that the most consistently excellent
popular magazines are: Wall Street Journal, NY Times, the New Yorker, and
my personal favorite, the Economist. I would stay away from Times - I
really do not like their writing style. As someone once made fun of their
awkward prose: "Backward ran sentences until reeled the mind [...] Where it
all will end, knows God!"
One other thing - while most Americans are fluent in their conversational
English - it does not mean that they are good at written English. In fact,
I would say that foreigners may have better mechanics, what they lack is
spontaneity and flow, which will only come with practice.
