Put statements in positive form.

In his Elements of Style, William Strunk wrote,

Make definite assertions. Avoid tame, colorless, hesitating, noncommittal language. Use the word not as a means of denial or in antithesis, never as a means of evasion.

Here are examples to show the difference ...

John was not very often on time. >>> John usually came late.
Lisa did not think that was a very nice thing to say. >>> Lisa thought that a mean thing to say.

Not is a weak word. Your readers want to know what is.

Certain uses of the negative help though. Placing a negative in opposition to a positive makes a stronger, clearer statement. Here is an example...

Your tone should be friendly and engaging, not distant or intimate.

And yet another…

Ask not what your country can do for you — ask what you can do for your country.