What is the best way, including software,  for non-native speaker of
English to correct pronunciation and accent?

By speaking with native speakers who are prepared to correct you.

I learned French at school in the UK and I thought I was pretty good.
Then when I went to France, I was told that I had an atrocious accent.

When I lived in Holland, I learned Dutch from a native teacher and he
was always correcting me. I'm sure that helped although I only rarely
needed to use my Dutch because most Dutch people speak such good
English. Nevertheless, they always wanted to practise their stuff on
me.

I concur with Probonopublico. No software could correct you better
than talking with a native speaker, and you'd fare better if this
person is an ESL (English-as-a-SEcond-Language) teacher who's been
trained in accent improvement techniques, or a diction teacher (like
the ones actors use when they have to adopt a different accent than
their own).

In addition, one very wise ESL teacher told me of a "free" method that
works to some extent. Listen to a movie in that language with the
accent you'd like to adopt and try to imagine you're the actor,
immitating their diction/speech. No Trainspotting or Gone with the
Wind there, or you'd end up with theatrical accent.

As an American who has spent most of 40 years living in Germany, I
agree heartily with Probono and Politicalguru.
It is very important to correct/improve you pronunciation as early as possible.
The longer you continue to speak with an accent, the more difficult it
will be to change your habits, and if you are among native speakers,
with time, they will become less aware of your accent, accepting that
that is just the way you speak, as they do with friends who have a
regional accent or perhaps a lisp, and no longer correcting you.
But you can help yourself to some extent by becoming aware of your
mistakes by making a recording of your reading aloud a text and then
comparing it with a native speaker's reading.  There may be material
for just this purpose, otherwise a "talking book" CD or other
recording could help.  And then as Politicalguru suggests, try to
imitate the native speaker's pronunciation, recording yourself.
If you are in a profession with its own special vocabulary, you should
master its pronunciation.

There are, however, website that address the subject, found with the search:
   improve OR correct pronunciation

For example:  
http://www.pronunciationpatterns.com/
http://esl.about.com/library/howto/htpronounce.htm
http://www.antimoon.com/perfectp/perfectp.htm

This one leads to other websites that I did not open:
http://ec.hku.hk/VEC/pronunciation/default.htm

And this one is also interesting:
http://www.fanetik.org/cpintro.html

If you are now in an English-speaking country, teachers of speech or
elocution could certainly help, as Politicalguru has suggested, and
may be necessary if there are some English sounds that you just cannot
get your tongue around, like R for many Chinese and Japanese.

Good luck!

To all of the above add this little tidbit, correct for the language
you are speaking in.

For instance, if your native tongue is French, Castillian, Italian or
any other Romance language to you phonology is smooth and flowing, the
words are all pronounced from the upper part of the larynx and out.
However, English, German, Arabian and other guttural languages have
many words that are pronounced from the lower part of the pharinx.
United Statesian English is CONSIDERABLY more guttural than it's
British counterpart, United Statesians (whether conciously or not)
make a concerted effort in making this difference as pronounced as
possible.

If you want to speak like a native United Statesian (or lessen the
difference) you must change the way in which you speak in English.
Make the words come from the bottom of your throat. The word
'American' lends itself very well for you to get a good idea of how
this works. If you touch your throat and say 'American' (assuming your
native tongue is a Romance one) you'll notice that the vibrations come
from the upper part of your throat, if you ask a native United
Statesian to do the same and touch his/her throat while he/she is
doing this, you'll notice that the vibrations that make the word come
from the bottom part of the throat. In order to sound more like a
United Statesian you must make all your words guttural, the more
guttural the sound the closer your speech will resemble that of United
Statesians. Also, the guttural speech will hide most imperfections in
your knowledge of the language.