For those who want to simplify the matter, affect  is always a verb (with some rare uses as a noun, including its special use in psychology), whereas effect  is usually a noun (though it has one use as a verb).  Given that the exceptions occur a very small percentage of the time, this basic distinction serves most of us quite well.  It is certainly better than making a random choice wherein the odds are that we would be right only 50% of the time.  A mnemonic device that mught work here is:  Affect designates Action; Effect denotes an Entity.  The weather affects us; the weather has an effect on us.

The definition of affect's rare use as a noun is "feeling or emotion, especially as manifested by facial expression or body language" (American Heritage Dictionary).  To illustrate this use, the dictionary cites Norman Mailer:  "The soldiers seen on television had been carefully chosen for blandness of affect."  It is also used in psychiatry and psychology to refer to "an expressed or observed emotional response," as in, "Restricted or blunted affect may be a symptom of mental illness, especially schizophrenia" (Random House [unabridged] Dictionary).  Few of us will have cause to use affect in this manner.

The use of effect as a verb, however, is more common than the use of affect as a noun.  It is actually an extension of the meaning of effect as a noun, in that it means "to bring about an effect."  The verbal definitions of effect in the American Heritage Dictionary are:  "to bring into existence, to produce a result, to bring about."  Thus, an organization may effect a new policy, or an individual may effect a plan.  Apart from this use as a verb, effect is a noun.

For further discussion and verification, see the online American Heritage Dictionary's usage note at this link – click here.